Bulletin of the Belgian Mathematical Society - Simon Stevin

Ricci curvature of integral submanifolds of an $f.p.k.$-space form

Mahmood Jaafari Matehkolaee

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Abstract

In this paper, relationships between the Ricci curvature and the squared mean curvature for integral submanifolds of an $f.p.k.$-space form by a basic inequality, are studied. We show that if an integral submanifold of maximum dimension of an $f.p.k.$-space form satisfies the equality case, then it must be minimal.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 3 (2014), 437-453.

Dates
First available in Project Euclid: 11 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1407765882

Digital Object Identifier
doi:10.36045/bbms/1407765882

Mathematical Reviews number (MathSciNet)
MR3250771

Zentralblatt MATH identifier
1305.53037

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53D10: Contact manifolds, general

Keywords
$f.p.k.$-space form Ricci curvature $k$-Ricci curvature Scalar curvature Integral submanifold $C$-totally real submanifold

Citation

Matehkolaee, Mahmood Jaafari. Ricci curvature of integral submanifolds of an $f.p.k.$-space form. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 3, 437--453. doi:10.36045/bbms/1407765882. https://projecteuclid.org/euclid.bbms/1407765882


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