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

Bang-Yen Chen, Adara M. Blaga and Gabriel-Eduard Vîlcu
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Bang-Yen Chen: Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Adara M. Blaga: Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
Gabriel-Eduard Vîlcu: Research Center in Geometry, Faculty of Mathematics and Computer Science, University of Bucharest, Topology and Algebra, Str. Academiei 14, 70109 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 4, 1-38

Abstract: 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.

Keywords: ? -invariants; Chen invariants; complex space form; inequality; squared mean curvature; ideal immersions; ? -Casorati curvatures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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