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A class of C-totally real submanifolds of Sasakian space forms

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Filip Defever ,
Ion Mihai  and
Leopold Verstraelen
Filip Defever
Affiliation:
Zuivere en Toegepaste Differentiaalmeetkunde, Department Wiskunde, K. U. Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium e-mail: filip.defever@wis.kuleuven.ac.be
Ion Mihai
Affiliation:
Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109 Bucharest, Romania e-mail: imihai@math.math.unibuc.ro
Leopold Verstraelen
Affiliation:
Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200 B, B - 3001 Leuven, Belgium, and Group of Exact Sciences, K.U. Brussel, Vrijheidslaan, 17 B - 1081 BrusselBelgium e-mail: leopold.verstraelen@wis.kuleuven.ac.be
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Abstract

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Recently, Chen defined an invariant δM of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M2m+1(C)satisfying Chen's equality.

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C40: Global submanifolds 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 1 , August 1998 , pp. 120 - 128
Copyright
Copyright © Australian Mathematical Society 1998

References

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