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

被引：10
作者：
Chen, Bang-Yen [1 ]
Blaga, Adara M. [2 ]
Vilcu, Gabriel-Eduard [3 ,4 ,5 ]
机构：
[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
[2] West Univ Timisoara, Dept Math, Timisoara 300223, Romania
[3] Univ Bucharest, Fac Math & Comp Sci, Res Ctr Geometry, Topol & Algebra, Str Acad 14, Bucharest 70109, Romania
[4] Univ Politehn Bucuresti, Fac Appl Sci, Dept Math & Informat, Splaiul Independentei 313, Bucharest 060042, Romania
[5] Petr Gas Univ Ploiesti, Dept Cybernet, Econ Informat Finance & Accountancy, Bd Bucuresti 39, Ploiesti 100680, Romania
来源：
MATHEMATICS | 2022年 / 10卷 / 04期
关键词：
delta-invariants; Chen invariants; complex space form; inequality; squared mean curvature; ideal immersions; delta-Casorati curvatures; PRODUCT CR-SUBMANIFOLDS; CHENS 1ST INEQUALITY; LAGRANGIAN SUBMANIFOLDS; WARPED PRODUCTS; ATTAINING EQUALITY; RIEMANNIAN SUBMERSIONS; ISOMETRIC IMMERSIONS; MINIMAL IMMERSIONS; PROJECTIVE SPACES; SHAPE OPERATOR;
D O I：
10.3390/math10040591
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 delta-invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on delta-invariants and their applications have been summarized in the first author's book published in 2011 Pseudo-Riemannian Geometry, delta-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 delta-invariants done mostly after the publication of the book.
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页数：38
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