多様体上の変換群、同変微分同相群のホモトピー型、
軌道空間上の可微分ベクトル場のなすリー環、多様体上の正則曲線、
対称空間の体積、対称空間上の微分形式の幾何学的性質、同変微分同相群と
その周辺の研究、最近は可微分軌道体の微分同相群およびLipschitz同相群を
主に研究している。
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Realization of spaces $E_6/(U(1)Spin(10)), E_7/(U(1)E_6),E_8/(U(1)E_7)$
and their volumes, Tokyo Jour. Math., 20 (1997), 73-86,
(with I. Yokota).
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Volumes of compact symmetric spaces, Tokyo Jour. Math., 20 (1997)
(with I. Yokota), 87-105.
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Invariant forms on the exceptional symmetric spaces FU and EV, Proceeding of 1996 Korea-Japan conference on transformation group theory, 3 (1997)
, 1-15, (with M. Matsubara).
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On the structure of the group of equivariant diffemorphisms of G-manifolds
with codimension one orbit, Topology 40 (2001), 1325-1337,(with K. Fukui)
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On the structure of the group of Lipschitz homeomorphisms and its
subgroups, Jour. Math. Soc. Japan 53 (2001), 501-511 (with K. Fukui)
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On the structure of automorphisms of manifolds, Proceeding
International Conference on Geometry, Integrability and Quantization,
(2000), 7-15 (with K. Fukui).
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On the moment maps of the compact classical hermitian symmetric spaces,
preprint (with H. Yoshida)
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On the first homology of the group of diffeomorphisms of smooth orbifolds
with isolated singularities., preprint (with K. Fukui)
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On the first homology of the group of equivariant Lipschitz
homeomorphisms of the plane with circle action,
京都大学数理解析研究所講究録 1290, (2002), 112-120.
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On the structure of the group of Lipschitz homeomorphisms and its
subgroups II, Jour. Math. Soc. Japan 55 (2003) 947 -- 956 (with K. Fukui).
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On the first homology of automorphism groups of
manifolds with geometric structures,
Central European Jour. Math. 3 (2005) 516 -- 528 (with K. Fukui).
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On the structure of the group of equivariant Lipschitz homeomorphisms of
G-manifolds with codimension one orbit,
Jour. Math. Soc. Japan 58 (2006) 1--16 (with K. Fukui and T. Miura).
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The first homology of the group of equivariant
diffeomorphisms and its applications, Journal of Topology 1 (2008) 461--476
(with K. Fukui).
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Commutators of $C^{\infty}$-diffeomorphisms preserving a submanifold,
Jour. Math. Soc. Japan 61 (2009) 427--436 (with K. Fukui).