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초록· 키워드
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We study Riemannian or pseudo-Riemannian manifolds which
admit a closed conformal vector field.
Subject to the condition that at each point $p\in M^n$ the set
of conformal gradient vector fields spans a non-degenerate
subspace of $T_pM$, using a warped product structure theorem we
give a complete description of the space of conformal vector
fields on arbitrary non-Ricci flat Einstein spaces.
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참고문헌 (13)
참고문헌 신청
/ 1925 / \ref\key 1 \by H. W. Brinkmann \paper Einstein spaces which aremapped conformally on each other \jour Math. Ann. \vol 94 \yr 1925 \pages 119--145 \endref
/ 1957 / \ref\key 22 \by K. Yano \book The theory of Lie derivatives andits applications \publaddr North-Holland
/ 1983 / \ref\key 18 \by B. O'Neill \book Semi-Riemannian geometry withapplications to relativity \publaddr Academic Press
/ 1985 / \ref\key 21 \by R. Sharma and K. L. Duggal\paper Acharacterization of affine conformal vector field \jour C. R.Math. Rep. Acad. Sci. Canada\vol 7 \yr 1985\pages 201
/ 1990 / \ref\key 20\by H. B. Rademacher \paper Generalized KillingSpinors with imaginary Killing function and conformal Killingfields Lecture Notes in Math. 1481 \publaddrS
/ 1957 / \ref\key 22 \by K. Yano \book The theory of Lie derivatives andits applications \publaddr North-Holland
/ 1983 / \ref\key 18 \by B. O'Neill \book Semi-Riemannian geometry withapplications to relativity \publaddr Academic Press
/ 1985 / \ref\key 21 \by R. Sharma and K. L. Duggal\paper Acharacterization of affine conformal vector field \jour C. R.Math. Rep. Acad. Sci. Canada\vol 7 \yr 1985\pages 201
/ 1990 / \ref\key 20\by H. B. Rademacher \paper Generalized KillingSpinors with imaginary Killing function and conformal Killingfields Lecture Notes in Math. 1481 \publaddrS
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