ON D-STARSHAPED SETS

H. K. El-Sayied (Egypt)

Received October 21, 2007

Abstract

The notions of starshaped and locally starshaped sets are extended, in Riemannian manifold, to D-starshaped and locally D-starshaped sets. Some results related to these generalized concepts are established in Riemannian manifold without conjugate points. Some illustrative examples are given to clarify the obtained results.

Keywords and phrases: conjugate points, minimal geodesic, D-convex sets, starshaped sets, supporting, locally supporting.