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Abstract:
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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 |