Chen-like Inequalities for Submanifolds in Kähler Manifolds Admitting Semi-Symmetric Non-Metric Connections

被引：0
|
作者：
Mihai, Ion [1 ]
Olteanu, Andreea [2 ]
机构：
[1] Univ Bucharest, Dept Math, Bucharest 010014, Romania
[2] Univ Agron Sci & Vet Med Bucharest, Dept Math Phys & Terr Measurements, Bucharest 011464, Romania
来源：
SYMMETRY-BASEL | 2024年 / 16卷 / 10期
关键词：
K & auml; hler manifold; complex space form; submanifolds; mean curvature; Ricci curvature; semi-symmetric connection; non-metric connection; Chen inequality; Euler inequality; SPACE-FORMS; SLANT SUBMANIFOLDS; SHAPE OPERATOR; CURVATURE;
D O I：
10.3390/sym16101401
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The geometry of submanifolds in K & auml;hler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen-Ricci inequality, Chen basic inequality, and a generalized Euler inequality for such submanifolds. These inequalities provide estimations of the mean curvature (the main extrinsic invariants) in terms of intrinsic invariants: Ricci curvature, the Chen invariant, and scalar curvature. In the proofs, we use the sectional curvature of a semi-symmetric, non-metric connection recently defined by A. Mihai and the first author, as well as its properties.
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页数：18
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