Abstract
In the geometry of submanifolds, Chen inequalities represent one of the most important tool to find relationships between intrinsic and extrinsic invariants; the aim is to find sharp such inequalities. In this paper we establish an optimal inequality for the Chen invariant δ ( 2 , 2 ) on Lagrangian submanifolds in quaternionic space forms, regarded as a problem of constrained maxima.
Highlights
Doctoral School of Mathematics, University of Bucharest, 010014 Bucharest, Romania; Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania
Lagrangian submanifolds are studied for their special geometric properties, and for their important roles in supersymmetric field theory and string theory. For these submanifolds in quaternionic space forms, we give an answer to one problem in submanifold theory, most precisely to find relationships between the main extrinsic invariants and intrinsic invariants
The same inequality holds for totally real submanifolds in complex space forms
Summary
Lagrangian submanifolds are studied for their special geometric properties, and for their important roles in supersymmetric field theory and string theory For these submanifolds in quaternionic space forms, we give an answer to one problem in submanifold theory, most precisely to find relationships between the main extrinsic invariants and intrinsic invariants. The intrinsic characteristics of a Riemannian manifold are given by its curvature invariants. In the case of a Lagrangian submanifold in a complex space form, we have the following relations. Is semipositive definite, where h is the second fundamental form of the submanifold Mn in M
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