Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants
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 <inline-formula><math xmlns="htt...
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MDPI AG
2022-02-01
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| author | Bang-Yen Chen Adara M. Blaga Gabriel-Eduard Vîlcu |
| author_facet | Bang-Yen Chen Adara M. Blaga Gabriel-Eduard Vîlcu |
| author_sort | Bang-Yen Chen |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants and their applications have been summarized in the first author’s book published in 2011 <i>Pseudo-Riemannian Geometry, δ-Invariants and Applications</i> (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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants done mostly after the publication of the book. |
| first_indexed | 2024-03-09T21:30:18Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:18Z |
| publishDate | 2022-02-01 |
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| spelling | doaj.art-3e19e85e69184800a835be100fe0160c2023-11-23T20:57:07ZengMDPI AGMathematics2227-73902022-02-0110459110.3390/math10040591Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants Bang-Yen Chen0Adara M. Blaga1Gabriel-Eduard Vîlcu2Department of Mathematics, Michigan State University, East Lansing, MI 48824, USADepartment of Mathematics, West University of Timişoara, 300223 Timişoara, RomaniaResearch Center in Geometry, Faculty of Mathematics and Computer Science, University of Bucharest, Topology and Algebra, Str. Academiei 14, 70109 Bucharest, RomaniaOne 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants and their applications have been summarized in the first author’s book published in 2011 <i>Pseudo-Riemannian Geometry, δ-Invariants and Applications</i> (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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-invariants done mostly after the publication of the book.https://www.mdpi.com/2227-7390/10/4/591<i>δ</i>-invariantsChen invariantscomplex space forminequalitysquared mean curvatureideal immersions |
| spellingShingle | Bang-Yen Chen Adara M. Blaga Gabriel-Eduard Vîlcu Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants Mathematics <i>δ</i>-invariants Chen invariants complex space form inequality squared mean curvature ideal immersions |
| title | Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants |
| title_full | Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants |
| title_fullStr | Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants |
| title_full_unstemmed | Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants |
| title_short | Differential Geometry of Submanifolds in Complex Space Forms Involving <i>δ</i>-Invariants |
| title_sort | differential geometry of submanifolds in complex space forms involving i δ i invariants |
| topic | <i>δ</i>-invariants Chen invariants complex space form inequality squared mean curvature ideal immersions |
| url | https://www.mdpi.com/2227-7390/10/4/591 |
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