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The aim of the present paper is to establish an \emph{intrinsic} generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.
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참고문헌 (10)
참고문헌 신청
J. Grifone / 1972 / Structure presque-tangente et connexions. I / Ann. Inst. Fourier 22(1):287~334
J. Grifone / 1972 / Structure presque-tangente et connexions. II / Ann. Inst. Fourier 22(3):291~338
F. Ikeda / 1981 / On S3- and S4-like Finsler spaces with the T-tensor of a special form / Tensor 35(3):345~351
J. Klein / 1968 / Formes ext´erieures g´en´eratrices de sprays / Ann. Inst. Fourier 18(1):241~260
B. N. Prasad / 1989 / On hv-recurrent Finsler connection / Indian J. Pure Appl. Math 20(8):790~798
J. Grifone / 1972 / Structure presque-tangente et connexions. II / Ann. Inst. Fourier 22(3):291~338
F. Ikeda / 1981 / On S3- and S4-like Finsler spaces with the T-tensor of a special form / Tensor 35(3):345~351
J. Klein / 1968 / Formes ext´erieures g´en´eratrices de sprays / Ann. Inst. Fourier 18(1):241~260
B. N. Prasad / 1989 / On hv-recurrent Finsler connection / Indian J. Pure Appl. Math 20(8):790~798
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