幾何学コロキウム Differential Geometry of CR-submanifolds and recent advancements

開催日時
2016年   6月 6日 16時 30分 ~   18時 00分
場所
3号館204室
講演者
Mohammad Hasan Shahid (Jamia Millia Islamia University)
 
Abstract : The notion of CR-submanifolds was introduced in 1978 by Aurel Bejancu. This branch of differential geometry has many interactions with other topics in mathematics with potential applications in mathematical physics. A CR-submanifold is endowed with two orthogonal complementary distributions such that one is holomorphic and the other is totally real. The study of these submanifolds plays an important role in diverse areas of differential geometry and relativity, as well as in mechanics. As far as its geometric point of view is concerned, the study has received the attention of a wide circle of mathematicians like B.Y. Chen, D.E.Blair, K. Sekigawa, Yano and Kon, S.Dragomir and M.Okumura et.al. A significant contribution is made by B. Y. Chen by giving some classification theorems and by generalizing some classical results. Later, various generalizations of the notion were obtained, namely, generic submanifolds, slant submanifolds and semi-slant submanifolds in Kaehler as well as in contact setting. In this talk, I will be speaking on CR-submanifolds starting from some elementary geometry of submanifolds and giving some interesting results about them up to some recent developments.

References:
A. Bejancu, “CR-submanifolds of a Kaehler manifold-I, II”, Proc. Amer. Math. Soc., 69 (1978), 134-142; Trans. Amer. Math. Soc., 69 (1978), 135-142.
B. Y. Chen, “CR-submanifolds of a Kaehler manifold-I, II”, J. Differential Geom., 16 (1981), 305-322; 16 (1981), 493-509.
M. Djoric and M. Okumura, “CR-submanifolds of Complex Projective Space”, Springer, 2010.
G. E. Vilcu, “Ruled CR-submanifolds of locally conformal Kaehler manifolds”, J. Geom. and Physics, 62 (2012), 1366-1372.
K. Yano and M. Kon, “Structures on manifolds”, Series in Pure Mathematics, 3, World Scientific, Singapore, 1984.


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