A+ CATEGORY SCIENTIFIC UNIT

Chen's inequality in the Lagrangian case

Volume 108 / 2007

Teodor Oprea Colloquium Mathematicum 108 (2007), 163-169 MSC: 53C21, 53C24, 53C25, 49K35. DOI: 10.4064/cm108-1-15

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.

Authors

  • Teodor OpreaFaculty of Mathematics and Informatics
    University of Bucharest
    Str. Academiei 14
    010014 Bucureşti, Romania
    e-mail

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