Browsing Mathematics by Author "Đorić, Mirjana"
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Đorić, Mirjana (Beograd , 1994)[more][less]
Abstract: It is an interesting problem to study the geometry of Riemannian manifolds by investigating the propetries of geometric objects on them. It turns out that the features of the geometry of a family of geometric objects on a Riemannian manifold strongly influence the geometry of the ambient space. In this paper we focus on the same kind of problems considering the extrinsic and intrinsic geometry of tubes about geodesics on Kahler and Sasakian manifolds. In order to obtain our results we mainly work with Jacobi vector fields because this falls among the best ways of analysing the geometry of normal and tubular neighborhoods. In Chapter II we compute the explicit formulas for the shape operator of tubes about co-geodesics on Sasakian space forms, using the technique of Jacobi vector fields. Further, in Chapter III we characterize locally Hermitian symmetric spaces and complex space forms considering the shape operator and the Ricci operator of tubes about geodesics on Kahler manifolds. Finally, in Chapter IV we characterize Sasakian space forms and locally co-symmetric spaces by analysing the action of the shape operator and the Ricci operator on tubes about cp-geodesics on Sa URI: http://hdl.handle.net/123456789/4091 Files in this item: 1
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