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null vectors, Bull. London Math. Soc. 34 (6), 650-658, 2002.
Kowalski, O. and Sekizawa, M. The Riemann extensions with cyclic parallel Ricci tensor,
Math. Nachr. 287 (8-9), 955-961, 2014.
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On twisted Riemannian extensions associated with Szabó metrics
Year 2017,
Volume: 46 Issue: 4, 593 - 601, 01.08.2017
Let $M$ be an n-dimensional manifold with a torsion free afine connection $\nabla$ and let $T^*M$ be the cotangent bundle. In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afine geometry of $(M,\nabla)$ and the neutral signature pseudo-Riemannian geometry of $T^*M$. We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.
Brozos-Vázquez, M., García-Rio, E., Gilkey, P., Nikevi¢, S. and Vázquez-Lorenzo, R. The
Geometry of Walker Manifolds, Synthesis Lectures on Mathematics and Statistics 5 (Morgan
and Claypool Publishers, 2009).
Calvino-Louzao, E, García-Rio, E., Gilkey, P. and Vázquez-Lorenzo, R. The geometry of
modied Riemannian extensions, Proc. R. Soc. A. 465, 2023-2040, 2009.
Calvino-Louzao, E., García-Rio, E. and Vázquez-Lorenzo, R. Riemann extensions of
torsion-free connections with degenerate Ricci tensor, Canad. J. Math. 62 (5), 1037-1057,
2010.
Diallo, A. S. and Massamba, F. Ane Szabó connections on smooth manifolds, Rev. Un.
Mat. Argentina 58 (1), 37-52, 2017.
Fiedler, B. and Gilkey, P. Nilpotent Szabo, Osserman and Ivanov-Petrova pseudo-
Riemannian manifolds, Contemp. Math. 337, 53-64, 2003.
García-Río, E., Gilkey, P., Nikcevi¢, S. and Vázquez-Lorenzo, R. Applications of Ane
and Weyl Geometry, Synthesis Lectures on Mathematics and Statistics 13 (Morgan and
Claypool Publishers, 2013).
García-Rio, E., Kupeli, D. N., Vázquez-Abal, M. E. and Vázquez-Lorenzo, R. Ane Osserman
connections and their Riemannian extensions, Dierential Geom. Appl. 11, 145-153,
1999.
Gilkey, P. B., Ivanova, R. and Zhang, T. Szabó Osserman IP Pseudo-Riemannian manifolds,
Publ. Math. Debrecen 62, 387-401, 2003.
Gilkey, P. and Stavrov, I. Curvature tensors whose Jacobi or Szabó operator is nilpotent on
null vectors, Bull. London Math. Soc. 34 (6), 650-658, 2002.
Kowalski, O. and Sekizawa, M. The Riemann extensions with cyclic parallel Ricci tensor,
Math. Nachr. 287 (8-9), 955-961, 2014.
Patterson, E. M. and Walker, A. G. Riemann extensions, Quart. J. Math. Oxford Ser. 3,
19-28, 1952.
Szabó, Z. I. A short topological proof for the symmetry of 2 point homogeneous spaces,
Invent. Math. 106, 61-64, 1991.
Yano, K. and Ishihara, S. Tangent and cotangent bundles: dierential geometry, Pure and
Applied Mathematics 16 ( Marcel Dekker, New York, 1973).
Diallo, A. S., Longwap, S., & Massamba, F. (2017). On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics, 46(4), 593-601.
AMA
Diallo AS, Longwap S, Massamba F. On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics. August 2017;46(4):593-601.
Chicago
Diallo, Abdoul Salam, Silas Longwap, and Fortuné Massamba. “On Twisted Riemannian Extensions Associated With Szabó Metrics”. Hacettepe Journal of Mathematics and Statistics 46, no. 4 (August 2017): 593-601.
EndNote
Diallo AS, Longwap S, Massamba F (August 1, 2017) On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics 46 4 593–601.
IEEE
A. S. Diallo, S. Longwap, and F. Massamba, “On twisted Riemannian extensions associated with Szabó metrics”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 4, pp. 593–601, 2017.
ISNAD
Diallo, Abdoul Salam et al. “On Twisted Riemannian Extensions Associated With Szabó Metrics”. Hacettepe Journal of Mathematics and Statistics 46/4 (August 2017), 593-601.
JAMA
Diallo AS, Longwap S, Massamba F. On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics. 2017;46:593–601.
MLA
Diallo, Abdoul Salam et al. “On Twisted Riemannian Extensions Associated With Szabó Metrics”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 4, 2017, pp. 593-01.
Vancouver
Diallo AS, Longwap S, Massamba F. On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics. 2017;46(4):593-601.