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

Filip Defever
Zuivere en Toegepaste Differentiaalmeetkunde
Departement Wiskunde
K. U. Leuven
Celestijnenlaan 200 B
B - 3001 Leuven
Belgium

and
Ion Mihai
Faculty of Mathematics
University of Bucharest
Str. Academiei 14
70109 Bucharest
Romania

and
Leopold Verstraelen
Departement Wiskunde
K. U. Leuven
Celestijnenlaan 200 B
B - 3001 Leuven
Belgium,
and
Group of Exact Sciences
K.U. Brussel
Vrijheidslaan 17
B - 1081 Brussel
Belgium

Abstract:

Recently, Chen defined an invariant $\delta_M$ 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 $\tilde M^{2m+1}(c)$ satisfying Chen's equality.

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© Copyright 1998, Australian Mathematical Society