On the projective geometry of sprays

Szilasi, József; Vattamány, Sz.

doi:10.1016/s0926-2245(00)00011-5

Cited by 10 publications

(7 citation statements)

References 12 publications

(14 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We recall (for details, see [52], [60], [61], [62]) that two sprays S and S over M are said to be (pointwise) projectively related, if there exists a function…”

Section: Projectively Related Spraysmentioning

confidence: 99%

See 1 more Smart Citation

On the projective theory of sprays with applications to Finsler geometry

Szilasi

2009

Preprint

View full text Add to dashboard Cite

show abstract

“…We recall (for details, see [52], [60], [61], [62]) that two sprays S and S over M are said to be (pointwise) projectively related, if there exists a function…”

Section: Projectively Related Spraysmentioning

confidence: 99%

“…An index-free description of the Douglas curvature is due to J. Szilasi and Sz. Vattamány [60]. They worked on the bundle τ T M : T T M → T M and applied the Frölicher-Nijenhuis formalism of vector-valued forms.…”

Section: Projectively Related Spraysmentioning

confidence: 99%

On the projective theory of sprays with applications to Finsler geometry

Szilasi

2009

Preprint

View full text Add to dashboard Cite

show abstract

“…Preliminaries 1.1. Throughout the paper we shall freely use the terminology and results of [14] and [15]. However, we collect some of the notations and definitions at this point for easy reference.…”

Section: Wherementioning

confidence: 99%

“…In a recent paper [15] J. Szilasi and the present author elaborated an intrinsic approach to the projective geometry of sprays and obtained compact, coordinate -free representations for the projectively invariant Douglas tensor. These results having been obtained, there arises an exciting question: possible to derive the above theorem intrinsically, using the technique developed in [15] and if so, how? The present paper is the outgrowth of attempts to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Projection onto the indicatrix bundle of a Finsler manifold

Vattamány¹

2001

Publ. Math. Debrecen

View full text Add to dashboard Cite

We present a simple geometric description of the process "projection onto the indicatrix bundle" of a Finsler manifold originally introduced by H. Izumi, in the framework of the theory whose foundations were laid by J. Grifone [7], [8]. Next we derive an intrinsic expression for the projection of the Douglas tensor and give a new proof of Sakaguchi's important observation that the projected Douglas tensor and the Douglas tensor vanish together. Finally we deduce a concise coordinate-free form for the mixed curvature of the "Landsberg-Douglas manifolds", and conlude that in n > 2 dimensions these manifolds are just the Berwald manifolds.

show abstract

“…Moreover, an intrinsic theory of projective changes (resp. semi-projective changes) has been investigated in [3], [12] (resp. [16]) following the KG-approach.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic theory of projective changes in Finsler geometry

Youssef

Abed

Soleiman

2011

Rend. Circ. Mat. Palermo

View full text Add to dashboard Cite

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]).

show abstract

On the projective geometry of sprays

Cited by 10 publications

References 12 publications

On the projective theory of sprays with applications to Finsler geometry

On the projective theory of sprays with applications to Finsler geometry

Projection onto the indicatrix bundle of a Finsler manifold

Intrinsic theory of projective changes in Finsler geometry

Contact Info

Product

Resources

About