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On sectional curvatures of a Weyl manifold. (English) Zbl 1125.53030

In [H. Pedersen and K. P. Tod, Adv. Math. 97, No. 1, 74–109 (1993; Zbl 0778.53041)], it is proved that if \(M\) is a compact positive-definite Einstein-Weyl manifold whose scalar curvature is everywhere strictly negative, then \(M\) is conformal to an Einstein manifold. In this paper, the author shows that if \(M\) is a Weyl manifold, of dimension \(>2\), such that at each point the sectional curvature is independent of the plane chosen, then \(M\) is locally conformal to an Einstein manifold.

MSC:

53C20 Global Riemannian geometry, including pinching
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citations:

Zbl 0778.53041

References:

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