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ALMOST r-CONTACT SEMI-SYMMETRIC METRIC FINSLER CONNECTION ON VECTOR BUNDLE

ALMOST r-CONTACT SEMI-SYMMETRIC METRIC FINSLER CONNECTION ON VECTOR BUNDLE DEMONSTRATE MATHEMATICAVol. XXVIIINo 31995K. K. DubeALMOST r-CONTACT SEMI-SYMMETRIC METRICFINSLER CONNECTION ON VECTOR B U N D L E1. IntroductionThe purpose of the present paper is to define almost r-contact semisymmetric metric Finsler connection on the total space V of the vectorbundle V(M) = (V,JI,M) and to study its various properties. In particular, they are studied for almost r-Sasakian semi-symmetric metric andr-Sasakian semi-symmetric metric Finsler connection on the total space ofthe vector bundle.Let V(M) = {F, II, M} be a vector bundle whose total space V is an(ra+m)-dimensional C°°-manifold and the base space M is an ra-dimensionalC°°-manifold. The projection map II : V —• Af, that is II (u) = X 6 M,for u e V, where u = (X,Y) and Y G Rm = II^(X),is the fibre of V(M)over X .A non-linear connection N on the total space V of V(M) is a differentiable distribution uNu G Tv(V) for u £ V such that(1.1)TU{V) = NU®wherev: = {XeTU(V) := 0}.Now Nu is called the horizontal and Vv the vertical distribution. Thusfor each X 6 TU(V) we can write(1.2)X = XH + XV,XHeNuandXvG V*.Let X*, i = 1 , 2 a n d ya, a = 1 , 2 , http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ALMOST r-CONTACT SEMI-SYMMETRIC METRIC FINSLER CONNECTION ON VECTOR BUNDLE

Dube, K. K.
Demonstratio Mathematica , Volume 28 (3): 8 – Jul 1, 1995
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Publisher
de Gruyter
Copyright
© by K. K. Dube
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1995-0304
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATE MATHEMATICAVol. XXVIIINo 31995K. K. DubeALMOST r-CONTACT SEMI-SYMMETRIC METRICFINSLER CONNECTION ON VECTOR B U N D L E1. IntroductionThe purpose of the present paper is to define almost r-contact semisymmetric metric Finsler connection on the total space V of the vectorbundle V(M) = (V,JI,M) and to study its various properties. In particular, they are studied for almost r-Sasakian semi-symmetric metric andr-Sasakian semi-symmetric metric Finsler connection on the total space ofthe vector bundle.Let V(M) = {F, II, M} be a vector bundle whose total space V is an(ra+m)-dimensional C°°-manifold and the base space M is an ra-dimensionalC°°-manifold. The projection map II : V —• Af, that is II (u) = X 6 M,for u e V, where u = (X,Y) and Y G Rm = II^(X),is the fibre of V(M)over X .A non-linear connection N on the total space V of V(M) is a differentiable distribution uNu G Tv(V) for u £ V such that(1.1)TU{V) = NU®wherev: = {XeTU(V) := 0}.Now Nu is called the horizontal and Vv the vertical distribution. Thusfor each X 6 TU(V) we can write(1.2)X = XH + XV,XHeNuandXvG V*.Let X*, i = 1 , 2 a n d ya, a = 1 , 2 ,

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 1995

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