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On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 16، دوره 41، شماره 2، بهمن 2009، صفحه 65-69 اصل مقاله (77.49 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2009.242 | ||
| نویسندگان | ||
| E. Peyghani؛ A. Tayebiii | ||
| چکیده | ||
| Let be an n-dimensional Riemannian manifold, and be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation induces an infinitesimal homothetic transformation on . Furthermore, the correspondence gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on onto the Lie algebra of infinitesimal homothetic transformations on , and the kernel of this homomorphism is naturally isomorphic onto the Lie algebra of infinitesimal isometries of . | ||
| کلیدواژه‌ها | ||
| Infinitesimal conformal transformation؛ homothetic transformation؛ Lagrange metric؛ isometry | ||
| عنوان مقاله [English] | ||
| On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric | ||
| چکیده [English] | ||
| Let be an n-dimensional Riemannian manifold, and be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation induces an infinitesimal homothetic transformation on . Furthermore, the correspondence gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on onto the Lie algebra of infinitesimal homothetic transformations on , and the kernel of this homomorphism is naturally isomorphic onto the Lie algebra of infinitesimal isometries of . | ||
| کلیدواژه‌ها [English] | ||
| Infinitesimal conformal transformation, homothetic transformation, Lagrange metric, isometry | ||
| مراجع | ||
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[1] M. T. K. Abbassi, Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g), Commnet. Math. Univ. Carolinae, 45 (4) (2004), 591-596. [2] H. Akbar-Zadeh, Transformations infinitesimals conformes des varietes finsleriennes compactes, Ann. Polon. Math., 36 (1979), 213-229. [3] M. Anastasiei, Locally conformal Kaehler structures on tangent manifold of a space form, Libertas Math., 19 (1999), 71-76. [4] I. Hasegawa and K. Yamauchi, Infinitesimal projective transformations on tangent bundles with lift connection, Scientiae Mathematicae Japonicae 52 (2003), 469-483. [5] R. Miron, and M. Anastasiei,, The Geometry of Lagrange spaces: Theory and applications, Kluwer Acad. Publ, FTPH, no.59,(1994). [6] R. Miron, and M. Anastasiei, Vector bundles and Lagrange spaces with application to Relativity. Geometry Balkan Press, Romania, (1981). [7] K. Yamauchi , On infinitesimal conformal transformations of the tangent bundles over Riemannian manifolds, Ann. Rep. Asahikawa. Med. Coll.Vol. 15. 1994. [8] K. Yano, The theory of Lie Derivatives and Its Applications, North Holland, (1957). [9] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, New York, (1973). [10] K. Yano and S. Kobayashi, Prolongations of tensor fields and connection to tangent bundle I, General theory, J. Math. Soc. Japan, 18 (1996), 194 -210.
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