The aim of the present paper is to provide an intrinsic investigation of projective changes in Finsler geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl torsion tensor, the Weyl curvature tensor and the Douglas tensor are investigated. The properties of these tensors and their interrelationships are obtained. Projective connections and projectively flat manifolds are characterized. The present work is entirely intrinsic (free from local coordinates) (arXiv:0904.1602 [math.DG]).

Integral formulas in riemannian geometry

Intrinsic theory of projective changes in Finsler geometry

Given a positive function F on Sn which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in Rn+1. We give some new characterizations of the Wulff shape by use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well-known results.

Integral formula of Minkowski type and new characterization of the Wulff shape

Geometrical and structural properties are proved for manifolds which are structured by the presence of a presymplectic form inducing a quasi-Sasakian structure.

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Contact transformation of a presymplectic form with Quasi-Sasakian structure

Harmonic and Killing forms on complete Riemannian manifolds

The purpose of the paper is to study Yamabe solitons on three-dimensional para-Sasakian, paracosymplectic and para-Kenmotsu manifolds. Mainly, we proved that *If the semi-Riemannian metric of a three-dimensional para-Sasakian manifold is a Yamabe soliton, then it is of constant scalar curvature, and the flow vector field V is Killing. In the next step, we proved that either manifold has constant curvature -1 and reduces to an Einstein manifold, or V is an infinitesimal automorphism of the paracontact metric structure on the manifold. *If the semi-Riemannian metric of a three-dimensional paracosymplectic manifold is a Yamabe soliton, then it has constant scalar curvature. Furthermore either manifold is $\eta$-Einstein, or Ricci flat. *If the semi-Riemannian metric on a three-dimensional para-Kenmotsu manifold is a Yamabe soliton, then the manifold is of constant sectional curvature -1, reduces to an Einstein manifold. Furthermore, Yamabe soliton is expanding with $\lambda$=-6 and the vector field V is Killing. Finally, we construct examples to illustrate the results obtained in previous sections.

Integral formulas in riemannian geometry

Citations

Intrinsic theory of projective changes in Finsler geometry

Integral formula of Minkowski type and new characterization of the Wulff shape

Contact transformation of a presymplectic form with Quasi-Sasakian structure

Harmonic and Killing forms on complete Riemannian manifolds

Yamabe Solitons on three-dimensional normal almost paracontact metric manifolds

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