Horizontal lift of symmetric connections to the bundle of volume forms ν

Anna Gąsior

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 1, page 45-61
  • ISSN: 2083-7402

Abstract

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In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.

How to cite

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Anna Gąsior. " Horizontal lift of symmetric connections to the bundle of volume forms ν ." Annales UMCS, Mathematica 64.1 (2010): 45-61. <http://eudml.org/doc/267845>.

@article{AnnaGąsior2010,
abstract = {In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.},
author = {Anna Gąsior},
journal = {Annales UMCS, Mathematica},
keywords = {Horizontal lift; π-conjugate connection; Killing field; infinitesimal transformation; F(3; 1)-structure; FK; FAK; FNK; FQK; FH-structure; horizontal lift; -conjugate connection; -structure},
language = {eng},
number = {1},
pages = {45-61},
title = { Horizontal lift of symmetric connections to the bundle of volume forms ν },
url = {http://eudml.org/doc/267845},
volume = {64},
year = {2010},
}

TY - JOUR
AU - Anna Gąsior
TI - Horizontal lift of symmetric connections to the bundle of volume forms ν
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 1
SP - 45
EP - 61
AB - In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.
LA - eng
KW - Horizontal lift; π-conjugate connection; Killing field; infinitesimal transformation; F(3; 1)-structure; FK; FAK; FNK; FQK; FH-structure; horizontal lift; -conjugate connection; -structure
UR - http://eudml.org/doc/267845
ER -

References

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  9. Miernowski A., Mozgawa W., Horizontal Lift to the Bundle of Volume Forms, Ann. Univ. Mariae Curie-Skłodowska Sect. A 57 (2003), 69-75. 
  10. Norden, A. P., Spaces with Affine Connection, Izdat. Nauka, Moscow, 1976 (Russian). Zbl0925.53007
  11. Radziszewski, K., π-geodesics and lines of shadow, Colloq. Math. 26 (1972), 157-163. Zbl0249.53010
  12. Rompała, W., Liftings of π-conjugate connections, Ann. Univ. Mariae Curie-Skłodowska Sect. A 32 (1978), 109-126. Zbl0466.53005
  13. Schouten, J. A., Ricci-Calculus, 2nd ed., Springer-Verlag, Berlin, Göttingen, Heidelberg, 1954. 
  14. Singh, K. D., Singh, R., Some f(3, ε)-structure manifolds, Demonstratio Math. 10 (1977), 637-645. Zbl0371.53030
  15. Yamauchi, K., On Riemannian manifolds admitting infinitesimal projective transformations, Hokkaido Math. J. 16 (1987), 115-125. Zbl0629.53040
  16. Yano, K., On structure defined by tensor field f of type (1, 1) satisfying f3 + f = 0, Tensor (N.S) 14 (1963), 99-109. Zbl0122.40705

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