- 1. Z. Afifi, Riemann extensions of affine connected spaces, Q. J. Math. Oxf. Ser., 5 (1954),
312-320.
- 2. S. Aslanci, S. Kazimova and A.A. Salimov, Some Remarks Concerning Riemannian
Extensions, Ukrainian Math. J., 62 (2010), 661-675.
- 3. C.L. Bejan and S. Eken, A characterization of the Riemann extension in terms of harmonicity, Czech. Math. J., 67 (2017), 197-206.
- 4. C.L. Bejan and O. Kowalski, On some differential operators on natural Riemann extensions, Ann. Glob. Anal. Geom., 48 (2015), 171-180.
- 5. L. Bilen, Projective vector fields on the cotangent bundle with modified Riemannian
extension, Journal of the Institute of Science and Technology 9 (2019), 389-396.
- 6. E. Calvino-Louzao, E. Garca-Ro, P. Gilkey and R. Vazquez-Lorenzo, The geometry of
modified Riemannian extensions, Proc. R. Soc. A, 465 (2009), 2023-2040.
- 7. E. Calvino-Louzao, E. Garca-Ro and R. Vazquez-Lorenzo, Riemann Extensions of
Torsion-Free Connections with Degenerate Ricci Tensor, Can. J. Math., 62 (2010), 1037- 1057.
- 8. J.C. Diaz-Ramos, E. Garcia-Rio and R. Vazquez-Lorenzo, New examples of Osserman
metrics with nondiagonalizable Jacobi operators, Differ. Geom. Appl., 24 (2006), 433- 442.
- 9. V. Dryuma, The Riemann Extensions in Theory of Differential Equations and their
Applications, Mat. Fiz. Anal. Geom., 10 (2003), 307-325.
- 10. A. Gezer, L. Bilen and A. Cakmak, Properties of modified Riemannian extensions, Zh.
Mat. Fiz. Anal. Geom., 11 (2015), 159-173.
- 11. I. Hasegawa and K. Yamauchi, Infinitesimal projective transformations on contact Riemannian manifolds, Journal of Hokkaido Univ. of Education, 51 (2000), 1-7.
- 12. I. Hasegawa and K. Yamauchi, infinitesimal projective transformations on tangent bundles with lift connections, Sci. Math. Jpn., 7 (2002), 489-503.
- 13. I. Hasegawa and K. Yamauchi, Infinitesimal projective transformations on tangent
bundles, M. Anastasiei et al. (eds.), Finsler and Lagrange Geometries Springer Science+Business Media, New York, 2003.
- 14. S. Kobayashi, A theorem on the affine transformation group of a Riemannian manifold,
Nagoya Math. J., 9 (1955), 39-41.
- 15. O. Kowalski and M. Sekizawa, On natural Riemann extensions, Publ. Math. Debrecen,
78 (2011), 709-721.
- 16. P. Law and Y. Matsushita, A spinor approach to Walker geometry, Commun. Math.
Phys., 282 (2008), 577-623.
- 17. T. Nagano, The projective transformation on a space with parallel Ricci tensor, Kodai
Math. Rep., 11 (1959), 131-138.
- 18. M. Okumura, On infinitesimal conformal and Projective transformation of normal contact spaces, Tohoku Math. J., 14 (1962), 389-412.
- 19. E.M. Patterson and A.G. Walker, Riemann extensions, Quart. J. Math. Oxford Ser.,
3(2) (1952), 19-28.
- 20. A.A. Salimov, Tensor Operators and Their Applications, Nova Science Publishers, New
York, 2012.
- 21. K. Yamauchi, On Riemannian manifolds admitting infinitesimal projective transformations, Hokkaido Math. J., 16 (1987), 115-125.
- 22. K. Yamauchi, On infinitesimal conformal transformations of the tangent bundles over
Riemannian manifolds, Ann. Rep. Asahikawa. Med. Coll., 16 (1995), 1-6.
- 23. K. Yamauchi, On infinitesimal projective transformations of the tangent bundles with
the complete lift metric over Riemannian manifolds, Ann. Rep. Asahikawa. Med. Coll., 19 (1998), 49-55.
- 24. K. Yamauchi, On infinitesimal projective transformations of tangent bundle with the
metric II+III, Ann. Rep. Asahikawa Med. Coll., 20 (1999), 67-72.
- 25. K. Yano, The Theory of Lie Derivatives and Its Applications, Bibliotheca mathematica,
North Holland Pub. Co., 1957.
- 26. K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, Inc., New
York, 1973.
- 27. K. Yano and S. Kobayashi, Prolongation of tensor fields and connections to tangent
bundles I, II, III, J. Math. Soc. Japan 18 (1966), 194-210, 236-246, 19 (1967), 486-488.
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