HORIZONTAL LIFT METRIC ON THE TANGENT BUNDLE OF A WEYL MANIFOLD
Abstract
Let (M; [g]) be a Weyl manifold and TM its tangent bundle equipped with
the horizontal lift of the base metric. The purpose of this paper is to study the tangent
bundle TM endowed with a Weyl structure, and obtain the ide under which conditions
such bundle is an Einstein-Weyl or a gradient Weyl-Ricci soliton.
Keywords
Full Text:
PDFReferences
M. T. K. Abbassi: g-natural metrics: new horizons in the geometry of tangent bundles of Riemannian manifolds. Note Mat., 28 (2009), 6–35.
M. T. K. Abbassi and M. Sarih: On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds. Differential Geom. Appl. 22 (2005), no. 1, 19–47.
C. L. Bejan and I. Gul: Sasaki metric on the tangent bundle of a Weyl manifold. Publ. Inst. Math (N.S.), 103 (2018), 25–32.
C. L. Bejan, S. E. Meric and E. Kilic: Gradient Weyl Ricci soliton. Turk J. Math. 44 (2020), 1137–1145.
D. Calderbank and H. Pedersen: Einstein-Weyl geometry. Surveys in Dif. Geo., 6 (2001), 387–423.
T. Higa: Weyl manifolds and Einstein-Weyl manifolds. Comment. Math. Univ. St. Pauli, 42 (2) (1993), 143–160.
O. Kowalski and M. Sekizawa: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles. A classification Bull. Tokyo Gakuei
Univ (4) 40 (1988), 1–29. Horizontal lift metric 7
M. Manev: Tangent bundles with complete lift of the base metric and almost hypercomplex Hermitian-Norden structure. C. R. Acad. Bulgare Sci., 3 (2014) 313–322.
H. Pedersen and K. P. Tod: Three dimensional Einstein-Weyl geometry. Adv. Math, 97 (1) (1993), 74-109.
K. Yano and S. Ishihara: Tangent and Cotangent Bundles. Marcel Dekker Inc., New York (1973).
DOI: https://doi.org/10.22190/FUMI210128066A
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)