We study some properties of Riemannian extensions in cotangent bundles with the help of adapted frames.
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References
E. M. Patterson and A. G. Walker, “Riemannian extensions,” Quant. J. Math., 3, 19–28 (1952).
K. Yano and Sh. Ishihara, “Tangent and cotangent bundles: Differential geometry,” Pure Appl. Math., No. 16 (1973).
V. Dryuma, “On Riemannian extension of the Schwarzschild metric,” Bull. Acad. Şti. Rep. Mold. Mat., No. 3, 92–103 (2003).
V. Dryuma, “The Riemannian extension in theory of differential equations and their application,” Mat. Fiz. Anal. Geom., 10, No. 3, 307–325 (2003).
G. T. Ganchev and A. V. Borisov, “Note on the almost complex manifolds with a Norden metric,” C. R. Acad. Bulg. Sci., 39, No. 5, 31–34 (1986).
M. Iscan and A. A. Salimov, On Kähler – Norden manifolds,” Proc. Indian Acad. Sci. (Math. Sci.), 119, No. 1, 71–80 (2009).
M. Manev and D. Mekerov, “On Lie groups as quasi-Kähler manifolds with Killing Norden metric,” Adv. Geom., 8, No. 3, 343–352 (2008).
A. A. Salimov, M. Iscan, and F. Etayo, “Paraholomorphic B-manifold and its properties,” Topol. Appl., 154, 925–933 (2007).
A. A. Salimov, M. Iscan, and K. Akbulut, “Some remarks concerning hyperholomorphic B-manifolds,” Chin. Ann. Math., 29, No. 6, 631–640 (2008).
V. V. Vishnevskii, “Integrable affinor structures and their plural interpretations,” J. Math. Sci., 108, No. 2, 151–187 (2002).
G. I. Kruchkovich, “Hypercomplex structures on a manifold, I,” Trudy Sem. Vect. Tens. Anal. Moscow Univ., 16, 174–201 (1972).
A. A. Salimov, Generalized Yano –Ako operator and the complete lift of tensor fields,” Tensor (N.S.), 55, No. 2, 142–146 (1994).
A. A. Salimov, “Lifts of poly-affinor structures on pure sections of a tensor bundle,” Rus. Math. (Izv. Vuzov), 40, No. 10, 52–59 (1996).
V. V. Vishnevskii, A. P. Shirokov, and V. V. Shurygin, Spaces over Algebras, Kazan Gos. Univ., Kazan (1985).
K. Yano and M. Ako, “On certain operators associated with tensor fields,” Kodai Math. Semin. Repts, 20, 414–436 (1968).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 579–590, May, 2010.
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Aslanci, S., Kazimova, S. & Salimov, A.A. Some remarks concerning Riemannian extensions. Ukr Math J 62, 661–675 (2010). https://doi.org/10.1007/s11253-010-0379-6
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DOI: https://doi.org/10.1007/s11253-010-0379-6