Ideal CR Submanifolds

Sasahara, Toru

doi:10.1007/978-981-10-0916-7_10

Geometry of Cauchy-Riemann Submanifolds 2016

DOI: 10.1007/978-981-10-0916-7_10

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Ideal CR Submanifolds

Toru Sasahara

Abstract: This paper surveys some of the known results on δ-ideal CR submanifolds in complex space forms, the nearly Kähler 6-sphere and odd dimensional unit spheres. In addition, the relationship between δ-ideal CR submanifolds and critical points of the λ-bienergy is mentioned. Some topics on variational problem for the λ-bienergy are also presented.2010 Mathematics Subject Classification. 53C42, 53B25.Let M be an n-dimensional submanifold of a Riemannian manifoldM . Let us denote by ∇ and∇ the Levi-Civita connections… Show more

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2022

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Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants

2022

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One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds. In order to establish such relations, the first author introduced in the 1990s the notion of δ-invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on δ-invariants and their applications have been summarized in the first author’s book published in 2011 Pseudo-Riemannian Geometry, δ-Invariants and Applications (ISBN: 978-981-4329-63-7). In this survey, we present a comprehensive account of the development of the differential geometry of submanifolds in complex space forms involving the δ-invariants done mostly after the publication of the book.

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Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants

2022

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Ideal CR Submanifolds

Cited by 1 publication

References 38 publications

Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants

Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants

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