TAILIEUCHUNG - Existence and uniqueness theorem for slant immersions in Kenmotsu space forms

In this paper we have obtained a general existence as well as uniqueness theorem for slant immersions into a Kenmotsu-space form. The purpose of the present paper is to establish a general existence and uniqueness theorem for slant immersions in Kenmotsu-space forms. | Turk J Math 33 (2009) , 409 – 425. ¨ ITAK ˙ c TUB doi: Existence and uniqueness theorem for slant immersions in Kenmotsu space forms Pradeep Kumar Pandey, Ram Shankar Gupta Abstract In this paper we have obtained a general existence as well as uniqueness theorem for slant immersions into a Kenmotsu-space form. Key Words: Kenmotsu manifold, slant immersion, mean curvature, sectional curvature. 1. Introduction B. Y. Chen has defined and studied slant immersions by generalizing the concept of holomorphic and totally real immersions [5]. Latter, it was A. Lotta [14], who introduced the concept of slant immersion of a Riemannian manifold into an almost contact metric manifold. B. Y. Chen and Y. Tazawa [8] have obtained examples of n-dimensional proper slant submanifolds in the complex Euclidean n-space C n . On the other hand, Chen and Vrancken [6] have established the existence of n-dimensional proper slant submanifolds into a non-flat ¯ n (4 c) and in contact geometry J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. complex space form M A. Fernandez [2] have established the existence and uniqueness theorem in Sasakian space form. Later, R. S. Gupta, S. M. K. Haider and A. Sharfuddin [10] have obtained the existence and uniqueness theorem into a non-flat cosymplectic space form. The purpose of the present paper is to establish a general existence and uniqueness theorem for slant immersions in Kenmotsu-space forms. In section 2, we review some basic formulae and results for our subsequent use. 2. Preliminaries Let M be a (2 m+1)-dimensional almost contact metric manifold with structure tensors (φ , ξ , η , g), where φ is a (1,1) tensor field, ξ a vector field, η a 1-form and g is the Riemannian metric on M . These tensors satisfy [1] 2000 AMS Mathematics Subject Classification: 53C25, 53C42. 409 PANDEY, GUPTA φ2 X = −X + η(X)ξ, φξ = 0, η(ξ) = 1, η(φX) = 0 () and g(φX, φY ) = g(X, Y ) − η(X)η(Y ), η(X) = g(X, ξ) ¯ , where T M ¯ denotes

• Toán học
• Kenmotsu manifold
• Slant immersion
• Mean curvature
• Sectional curvature
• Kenmotsu space forms
• Warped product
• Slant submanifold
• Semi slant submanifold
• Canonical structure
• Lightlike hypersurface
• Kenmotsu space form
• Non existence
• Indefinite Kenmotsu space
• Semi Riemannian manifold
• Anti invariant
• Semi slant
• η Einstein lightlike hypersurfaces
• Indefinite Kenmotsu manifold
• Relative nullity foliation
• Screen distribution
• Nullity distributions
• Riemannian submersion
• conformal submersion