Geodesic
Chen's inequality in the Lagrangian case
Teodor Oprea1
1 Faculty of Mathematics and Informatics University of Bucharest Str. Academiei 14 010014 Bucureşti, Romania
Colloquium Mathematicum, Tome 108 (2007) no. 1, pp. 163-169.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm108-1-15
Keywords: theory submanifolds following problem fundamental establish simple relationships between main intrinsic invariants main extrinsic invariants submanifolds basic relationships discovered until inequalities analyze problems follow idea udri method constrained extremum natural prove geometric inequalities improve chens inequality which characterizes totally real submanifold complex space form suppose submanifold lagrangian formulate analyze suitable constrained extremum problem

Teodor Oprea 1

1 Faculty of Mathematics and Informatics University of Bucharest Str. Academiei 14 010014 Bucureşti, Romania 
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Teodor Oprea. Chen's inequality in the Lagrangian case. Colloquium Mathematicum, Tome 108 (2007) no. 1, pp. 163-169. doi : 10.4064/cm108-1-15. http://geodesic.mathdoc.fr/articles/10.4064/cm108-1-15/

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