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Book Review: Geometry of CR-submanifolds [PDF]
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CR submanifolds in holomorphic statistical manifolds
(主査) 准教授 古畑 仁, 教授 泉屋 周一, 教授 大本 亨 理学院(数学専攻)
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Submersions of CR Submanifolds
2016O’Neill introduced the notion of Riemannian submersions (cf. O’Neill, Mich. Math. J. 13, 459–469, 1966, [28]). For the submersion \(\pi :M\longrightarrow N\) of a CR submanifold M of a Kaehler manifold \(\bar{M}\) onto an almost Hermitian manifold N, Kobayashi (cf. Kobayashi, Tohoku Math. J.
Mohammad Hasan Shahid +2 more
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2016
This chapter surveys some of the known results on \(\delta \)-ideal CR submanifolds in complex space forms, the nearly Kahler 6-sphere and odd dimensional unit spheres. In addition, the relationship between \(\delta \)-ideal CR submanifolds and critical points of the \(\lambda \)-bienergy functional is mentioned.
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This chapter surveys some of the known results on \(\delta \)-ideal CR submanifolds in complex space forms, the nearly Kahler 6-sphere and odd dimensional unit spheres. In addition, the relationship between \(\delta \)-ideal CR submanifolds and critical points of the \(\lambda \)-bienergy functional is mentioned.
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Paraquaternionic CR-Submanifolds
2016Paraquaternionic structures, at first known as quaternionic structures of second kind, are due to P. Libermann. Their study parallels that of quaternionic manifolds, yet relies on the algebra of paraquaternionic numbers. The counterpart in odd dimension of a paraquaternionic structure was introduced in 2006 by S. Ianus, R. Mazzocco and G.E.
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Lorentzian geometry of CR submanifolds
Acta Applicandae Mathematicae, 1989A. Bejancu defined CR submanifolds of differentiable manifolds with a (positive definite) Riemannian metric and almost Hermitian structure as a generalization of holomorphic submanifolds and totally real submanifolds. In this article, the notion of CR submanifold is extended to orientable Lorentz submanifolds of semi-Riemannian manifolds with an almost
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Lorentzian Geometry and CR-Submanifolds
2016This paper contains an up-to-date information on the Lorentzian geometry of CR-submanifolds, contact CR-submanifolds and globally framed CR-submanifolds (M, g) of an indefinite semi-Riemannian manifold. In view of the large number of excellent paper appearing in this field, we focus on those key results whose Lorentzian geometry is different than their
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