Chen's inequality in the Lagrangian case

Teodor Oprea

Colloquium Mathematicae (2007)

  • Volume: 108, Issue: 1, page 163-169
  • ISSN: 0010-1354

Abstract

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In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form. For that we suppose that the submanifold is Lagrangian and we formulate and analyze a suitable constrained extremum problem.

How to cite

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Teodor Oprea. "Chen's inequality in the Lagrangian case." Colloquium Mathematicae 108.1 (2007): 163-169. <http://eudml.org/doc/283641>.

@article{TeodorOprea2007,
abstract = {In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form. For that we suppose that the submanifold is Lagrangian and we formulate and analyze a suitable constrained extremum problem.},
author = {Teodor Oprea},
journal = {Colloquium Mathematicae},
keywords = {complex space form; Lagrangian submanifold; mean curvature; Chen's inequality},
language = {eng},
number = {1},
pages = {163-169},
title = {Chen's inequality in the Lagrangian case},
url = {http://eudml.org/doc/283641},
volume = {108},
year = {2007},
}

TY - JOUR
AU - Teodor Oprea
TI - Chen's inequality in the Lagrangian case
JO - Colloquium Mathematicae
PY - 2007
VL - 108
IS - 1
SP - 163
EP - 169
AB - In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form. For that we suppose that the submanifold is Lagrangian and we formulate and analyze a suitable constrained extremum problem.
LA - eng
KW - complex space form; Lagrangian submanifold; mean curvature; Chen's inequality
UR - http://eudml.org/doc/283641
ER -

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