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초록· 키워드
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In this paper, we shall prove several results concerning Ricci curvature of a
Riemannian manifold (M,g): =(SU(2), g) with an arbitrary given left invariant metric g.
First of all, we obtain the maximum (resp. minimum) of { r(X) := Ric(X,X) | ||X||_g =1, X∈Χ(M) } where $Ric$ is the Ricci tensor field on (M,g), and then get a necessary and sufficient condition
for the Levi-Civita connection ▽ on the manifold (M,g) to be projectively flat.
Furthermore, we obtain a necessary and sufficient condition for the Ricci curvature r(X)
to be always positive (resp. negative), independently of the choice of unit vector field X.
목차
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참고문헌 (9)
참고문헌 신청
A. L. Besse / 1987 / Einstein Manifolds / Springer-Verlag
J. A.Wolf / 1964 / Curvature in nilpotent Lie groups / Proc. Amer. Math. Soc. 15 : 271 ~ 274
J. Milnor / 1976 / Curvatures of left invariant metrics on Lie groups / Advances in Math. 21 (3) : 293 ~ 329
J.-S. Park / 1990 / Harmonic inner automorphisms of compact connected semisimple Lie groups / Tohoku Math. J. 42 (1) : 83 ~ 91
J.-S. Park / 1996 / The Abbena-Thurston manifold as a critical point / Canad. Math. Bull 39 (3) : 352 ~ 359
J. A.Wolf / 1964 / Curvature in nilpotent Lie groups / Proc. Amer. Math. Soc. 15 : 271 ~ 274
J. Milnor / 1976 / Curvatures of left invariant metrics on Lie groups / Advances in Math. 21 (3) : 293 ~ 329
J.-S. Park / 1990 / Harmonic inner automorphisms of compact connected semisimple Lie groups / Tohoku Math. J. 42 (1) : 83 ~ 91
J.-S. Park / 1996 / The Abbena-Thurston manifold as a critical point / Canad. Math. Bull 39 (3) : 352 ~ 359
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