Pointwise slant submanifolds in almost Hermitian manifolds

An interesting class of submanifolds of almost Hermitian manifolds (\tilde M,\tilde g,J) is the class of slant submanifolds. Slant submanifolds were introduced by the first author in [6] as submanifolds M of (\tilde M,\tilde g,J) such that, for any nonzero vector X \in TpM, p \in M, the angle q(X) between JX and the tangent space TpM is independent of the choice of p\in M and X \in TpM. The first results on slant submanifolds were summarized in the book [7]. Since then slant submanifolds have been studied by many geometers. Many nice results on slant submanifolds have been obtained during the last two decades. The main purpose of this paper is to study pointwise slant submanifolds in almost Hermitian manifolds which extends slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper.

Anahtar Kelimeler:

Slant submanifold, pointwise slant submanifold, slant function, conformal mapping, cohomology

Pointwise slant submanifolds in almost Hermitian manifolds

Keywords:

Slant submanifold, pointwise slant submanifold, slant function, conformal mapping, cohomology,

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Department of Mathematics, Michigan State University, East Lansing, Michigan 48824–1027, USA e-mail: bychen@math.msu.edu Oscar J. GARAY
Departamento de Matematicas, Facultad de Ciencia y Tecnologia, Universidad del Pais Vasco, Apartado 644, Bilbao 48080, SPAIN e-mail: oscarj.garay@ehu.es