General Mathematics, Vol. 5, No. 1 - 4, pp. 385-392, 1995

K. Trencevski -- Principal Directions for Submanifolds Imbeded in Euclidean Spaces of Arbitrary Codimension

Abstract: In a recent paper [4] are introduced principal directions of a locally imbedded $ n $-dimensional manifold in $ \Bbb R^{n+k} $, which generally are not intrinsically defined. In this paper are introduced another two definitions of principal directions using sectional curvature and Ricci tensor, which are intrinsically defined. Some basic results about hypersurfaces are proven. Further, there are considered some special cases when some of the these principal directions coincide.

Classification (MSC91): 53A07, 53B25

Keywords: 53A07, 53B25

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