Classification of δ(2,n− 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

Chen, Bang‐Yen; Dillen, Franki; Veken, Joeri Van der; Vrancken, Luc

doi:10.1016/j.jmaa.2017.10.044

Cited by 10 publications

(6 citation statements)

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“…This is the simplest case of ideal Lagrangian submanifold with ∑ k i=1 n i = n. The δ(2, n − 2)-ideal Lagrangian submanifolds in a complex space form have been studied and completely classified in [65]. Here, we present the classification theorem for ideal Lagrangian submanifolds merely in C n .…”

Section: δ(N − 1)-ideal Lagrangian Submanifoldsmentioning

confidence: 99%

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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Section: δ(N − 1)-ideal Lagrangian Submanifoldsmentioning

confidence: 99%

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

2022

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“…Totally real and, particularly, Lagrangian submanifolds in Kähler manifolds, complex space forms, etc. have been explored widely (see, for instance, [25][26][27][28][29][30][31]). However, not much is known about totally real and Lagrangian submanifolds in para-Kähler manifolds.…”

Section: Introductionmentioning

confidence: 99%

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Chen

Decu

Vîlcu

2021

Entropy

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“…Later, he proposed the extended version of these optimal inequalities for different submanifolds of different manifolds (see [9] and the references therein). The Chen ideal submanifolds have also been investigated (see [4,11,12]).…”

Section: Introductionmentioning

confidence: 99%

Optimal inequalities for submanifolds in statistical manifolds of quasi constant curvature

Bansal

Uddin

Shahid

2021

Filomat

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In this paper, we establish B.-Y. Chen?s optimal inequalities for statistical submanifolds involving Casorati curvature and the normalized scalar curavture in a statistical manifold of quasi constant curvature. The equality cases of these inequalities are also considered. Further, we provide some applications of our results. Moreover, as a new example we construct minimal statistical surface (statistical submanifold) of a statistical manifold of quasi constant curvature.

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Classification of δ(2,n− 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

Abstract: It was proven in [13] that every Lagrangian submanifold M of a complex space form M n (4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality:

Cited by 10 publications

References 10 publications

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

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

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Optimal inequalities for submanifolds in statistical manifolds of quasi constant curvature

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