Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 25, No. 1, pp. 137-144 (2009)

Legendrian warped product submanifolds in generalized Sasakian space forms

Andreea Olteanu

University of Bucharest, Romania

Abstract: Recently, K. Matsumoto and I. Mihai established a sharp inequality for warped products isometrically immersed in Sasakian space forms. As applications, they obtained obstructions to minimal isometric immersions of warped products into Sasakian space forms.

P. Alegre, D.E. Blair and A. Carriazo have introduced the notion of generalized Sasakian space form.

In the present paper, we obtain a sharp inequality for warped products isometrically immersed in generalized Sasakian space forms. Some applications are derived.

Keywords: Warped product, Laplacian, mean curvature, Legendrian submanifold, generalized Sasakian space form

Classification (MSC2000): 53C40; 53C25

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