My Works
Reserch Papers (October 27, 2023)
- On transversely flat conformal foliations with good measures, Trans. Amer. Soc. 348 (1996), 1939-1958.
- Classification of Riemannian flows with transverse similarity structures, Ann. Fac. Sci. Toulouse Vol.VI, no.2 (1997), 203-227.
- Invariance of the Godbillon-Vey class by C1-diffeomorphisms for higher codimensional foliations, Jour. Math. Soc. Japan Vol.51, No.3 (1999), 655-660.
- On transversely flat conformal foliations with good measures II, Hiroshima Math. Jour. Vol.28, No.3 (1998), 523-525.
- On the Real Secondary classes of transversely holomorphic foliations, Ann. Inst. Fourier, Vol.50, No.3 (2000), 995-1017.
- On the real secondary classes of transversely holomorphic foliations II, Tôhoku Math. J. 55 (2003), 361-374.
- A Remark on the Bott class, Ann. Fac. Sci. Toulouse Vol. X, no.1 (2001), 5-21.
- Localization and Residue of the Bott class, Topology, Vol.43 (2004), 289-317.
- Complexification of foliations and Complex secondary classes, Bull. Braz. Math. Soc, NS Vol.34, No.2 (2003), 251-262.
- Residues of the Bott class and an application to the Futaki invariant, Asian J. Math., Vol.7, No.2 (2003), 239-268.
- On Quasiconformal Deformations of Transversely Holomorphic Foliations, Jour. Math. Soc. Japan, Vol. 57, No.3 (2005), 725-734.
- Infinitesimal derivative of the Bott class and the Schwarzian derivatives, Tohoku Math. J., Vol.61 (2009), 393-416.
- A Fatou-Julia decomposition of transversally holomorphic foliations, Ann. Inst. Fourier (Grenoble), Vol. 60 (2010), 1057-1104.
- On Fatou-Julia decompositions, Ann. Fac. Sci. Toulouse, Vol. 22 (2013), 155-195.
- On independent rigid classes in H*(WUq), Illinois J. of Math., Vol. 56 (2012), 1001-1343 (actually appeared in 2014).
- Transverse projective structures of foliations and infinitesimal derivatives of the Godbillon-Vey class, Internat. J. Math., Vol.26 (2015), 1540001, 29pp, Shoshichi Kobayashi Memorial Volume
- Derivatives of secondary classes and 2-normal bundles of foliations, J. Math. Sci. Univ. Tokyo, Vol.22 (2015), The special issue for the 20th anniversary, 893-937.
- Notes on `Infinitesimal derivative of the Bott class and the Schwarzian derivatives', Tohoku Math. J., Vol.69 (2017), 129-139.
- On Fatou and Julia sets of foliations, J. Math. Soc. Japan, Vol. 72 (2020), 1145-1159.
- On a characteristic class associated with deformations of foliations, Internat. J. Math, Vol. 34 (2023), 2350003.
A preprint is available at arXiv:2011.04340.
- Formal frames and deformations of affine connections, preprint ('22/5/30).
Also available at arXiv:2206.00336, to appear in Tohoku Math. Jour.
- Notes on projective structures with torsion, preprint ('23/1/12), under a major revision.
Also available at arXiv:2301.04516.
Monograph (October 20, 2021)
- Godbillon-Vey class of transversely holomorphic foliations, MSJ memoirs vol. 24, June 2010.
Survey articles (September 8, 2017)
* means the article is not refereed: it applies to 2, 6, 7, 8 and 9.
- Some results on secondary characteristic classes of transversely holomorphic foliations, in `Foliations: GEOMETRY AND DYNAMICS', pp. 3-16, World Scientific Publishing, Singapore, 2002.
- On existence and quasiconformal deformations of transversely holomorphic foliations* (PDF File, 64kbytes), Sūrikaisekikenkyūsho Kōkyūroku, Complex Dynamics, No. 1447 (2005), 15-19.
This article is a survey for the paper 11 above, and is a note for the talk 6 below.
- On infinitesimal derivatives of the Bott class, in `Foliations 2005', pp. 37-46, World Scientific Publishing, Singapore, 2006.
This is a survey for the paper 12 above, and is a note for the talks 7 and 8 below.
- On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, Advanced Studies in Pure Mathematics, Vol.56 (2009), pp. 39-47, Mathematical Society of Japan.
This is an announcement for the paper 13 above, and is based on the talks 11 and 12 below.
- On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, in `Differential Geometry', Proceedings of the VIII International Colloquium Santiago de Compostela, Spain, 7-11 July 2008, World Scientific (2009), pp. 65-74.
This is a brief survey for the paper 13 above, and is based on the talk 14 below.
This article contains a few number of new results.
- On the Fatou-Julia decomposition of complex codimension-one transversely holomorphic foliations* (in Japanese, PDF File, 208kbytes), RIMS Kokyuroku No. 1661, Differential geometry of foliations and related topics on the Bergman kernel, July 2009, pp. 1-20.
This is an article based on the talk in a conference held at RIMS, Kyoto in Dec. 2008.
- On Fatou-Julia decompositions of pseudosemigroups* (PDF File, 85kbytes), RIMS Kokyuroku No. 1699, Integrated Research on Complex Dynamics and its Related Fields, July 2010, 137-143.
This is a survey for the paper 14 above, and based on a talk given at `2009 Complex Dynamics conference - Integrated Research on Complex Dynamics and its Related Fields -'.
- On Fatou-Julia decompositions of pseudosemigroups II* (PDF File, 101kbytes), RIMS Kokyuroku No. 1762, Research on Complex Dynamics and Related Fields, Nov. 2011, 125-133.
This is a survey on the paper 14 above, and based on a talk given at `2010 Complex Dynamics conference - Integrated Research on Complex Dynamics and its Related Fields -'.
- Independence and non-triviality of rigid secondary complex characteristic classes* (PDF File, 87kbytes), RIMS Kokyuroku No. 1807, Integrated Research on Complex Dynamics, Sep. 2012, 74-79.
This is a survey on the paper 15 above, and based on a talk given at `Complex Dynamics Conference of Academic Year 2011-2012 - Integrated Research on Complex Dynamics -'.
- On linear independence of classes in H*(WUq) (PDF File, 84kbytes), Jan. 2013.
Accepted in the proceedings volume of GF2012 but not appeared by some reason (which I do not know).
I have no plan to submit this article so that I will leave it here for the moment.
This is a review on the paper 15, and is based on the talk 11 below.
- On deformations and rigidity of the Godbillon-Vey class, Geometry, Dynamics, and Foliations 2013, Advanced Studies in Pure Mathematics 72, 2017, 1-18.
- On the Fuks–Lodder–Kotschick class for deformations of foliations, Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021, 2021, 1-15.
This is a review on the paper 20, and is based on the talk 17 below.
Translations (September 8, 2017)
- On Thurston's construction of a surjective homomorphism H2n+1(BΓn,Z)→R, Tadayoshi Mizutani,Geometry, Dynamics, and Foliations 2013, Advanced Studies in Pure Mathematics 72, 2017, 211-219.
Originally published in RIMS Kokyuroku No. 286 (the original article is written in Japanese).
This article is refereed although it is a tranlation.
Thesis (appeared as research papers 5 and 6)
- On the real secondary classes of transversely holomorphic foliations, thesis, Univ. Tokyo, 1998.
Talks at international conferences (July 17, 2023)
- The secondary characteristic classes of transversaly holomorphic foliations, at Complex Analysis in Dynamical Systems, IMPA-Rio de Janeiro, September 3, 1998.
- The Godbillon-Vey class of transversaly holomorphic foliations, at Foliations: Geometry and Dynamics, Banach Center (Warsaw), June 8, 2000.
- Residues of the Bott class, at New Directions in Dynamical Systems, Ryukoku University and Kyoto University, August 7, 2002.
- Residues of the Bott class, at Geometry and Foliations 2003 at Ryukoku University, 2003/9/11.
- Existence of transversely holomorphic structure of complex codimension one, at Topological and geometrical methods of complex differential equations, RIMS (Research Institute for Mathematical Sciences), Kyoto University, 2004/1/21.
- Infinitesimal derivative of the Bott class and the Schwarzian derivative, Foliations 2005, Wydział Matematyki Uniwersytetu Łódzkiego (Faculty of Mathematics of University of Lodz), Łódź (Lodz in Poland), 2005/6/14.
- On the Julia-Fatou decomposition of complex codimension-one folitaions, Niigata Workshop on Complex Geometry and Singularities, CrossPal Niigata, Niigata, 2007/8/24.
- A Fatou-Julia decomposition of complex codimension-one foliations, Global and Local Aspects of Holomorphic Foliations. In Honor of the 60th Birthday of Alcides Lins Neto, IMPA, Angra dos Reis, 2008/02/15.
- On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one, VIII International Colloquium on Differential Geometry, Santiago de Compostela (7-11 July, 2008), 2008/07/11.
- Infinitesimal deformations of foliations and Cartan connections, Geometry and Dynamics, Todai Forum 2011, UMPA ENS-Lyon, 2011/10/17.
- On independent rigid classes in H*(WUq), Foliations 2012, Wydział Matematyki i Informatyki, Uniwersytetu Łódzkiego (Faculty of Mathematics and Computer Science, University of Lodz), Łódź (Lodz in Poland), 2012/6/27.
- On Fatou-Julia decompositions of complex dynamical systems, Geometry and Foliations 2013, Graduate School of Mathematical Sciences, University of Tokyo, 2013/9/9. abstract
- Construction of secondary characteristic classes for foliations using the Chern-Weil theory, BGamma School, Faculty of Science and Engineering, Chuo University, 2013/9/18,19.
- Derivatives of the Godbillon-Vey class and transverse projective structures of foliations, 29th Summer Conference on TOPOLOGY and its APPLICATIONS (Sumtopo2014), College of Staten Island, 2014/7/23.
- A Chern-Weil construction for derivatives of characteristic classes, Foliations 2016, Będlewo (Poland), 2016/7/16.
- A remark on the Fatou sets of foliations of CP2, Complex foliations, dynamics and geometry, Universidade Federal Fluminense, Niterói, Rio de Janeiro (Brasil), 2018/7/24.
- On the Fuks-Lodder-Kotschick class for deformations of foliations, Contemporary Mathematics in Kielce 2020, Katedra Matematyki, Wydział Nauk Ścisłych i Przyrodniczych, Uniwersytetu Jana Kochanowskiego w Kielcach, Kielce (Poland), 2021/2/24 (planned in 2020 but held in 2021).
- On the structure of characteristic classes of codimension-one foliations, 36th Summer Topology Conference, July 18-22, 2022, University of Vienna, Department of Mathematics (Austria), 2022/7/18.
- Some metric-like tensors for pseudo(semi)groups, Current themes in complex dynamics, July 3-7, 2023, Institut de Mathématiques, Université Toulouse (France), '23/7/4. Abstract (corrected typos).
Talks at seminars abroad (September 8, 2017)
- Secondary characteristic classes of Transversely holomorphic foliations of complex codimension one, at Aarhus Universitet, March 13, 2000.
- Des dérivées infinitésimales de la classe de Bott et les dérivées schwarziennes, Le Séminaire de Mathématiques Pures, Unité de mathématiques pures et appliquées, École normale supérieur de Lyon, 2005/6/29.
- An introduction to secondary classes of foliations, Differential Geometry and Foliation Seminar, Centro de Investigacion en Matematicas (CIMAT), Guanajuato (Mexico), 2006/2/13.
- An introduction to secondary classes of foliations, Seminario de Sistemas Dinamicos y Ecuaciones Diferenciales, Instituto de Matemáticas, Unidad Morelia, Morelia (Mexico), 2006/2/20.
- Sur la décomposition Fatou-Julia de feuilletages transversalement holomorphes de complex codimension un, Analyse, géométrie et dynamique complexes, Laboratoire Emile Picard, Université Paul Sabatier, 2007/11/22.
- Sur la décomposition de Fatou-Julia d'un feuilletage transversalement holomorphes de codimension complex 1, Séminaire Géométrie - Topologie Dynamique, Département de Mathématiques de la Faculté des Sciences d'Orsay, 2009/03/18.
- Une construction de mesures δ-conformes pour des feuilletages transversalement holomorphes de codimension complexe 1, Dynamique et Géométrie complexes, Département de Mathématiques de la Faculté des Sciences d'Orsay, 2009/03/20.
- Autour de la décomposition de Fatou-Julia, Séminaire (Systèmes Dynamiques), Institut de Mathématiques de Toulouse, 2013/10/25.
- Autour de la décomposition de Fatou-Julia, Groupe de travaille ``Théorie ergodique et syetèmes dynamiques'', Département de Mathématiques d'Orsay (Paris), 2013/11/4.
- Autour de la décomposition de Fatou-Julia, Séminaires de Géométrie analytique, Institut de recherche mathématique de Rennes (Rennes), 2013/11/28.
- Quelques exemples de décomposition de Fatou-Julia pour des champs de vecteurs, Séminaire (Systèmes Dynamiques), Institut de Mathématiques de Toulouse (Toulouse), 2013/12/6.
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