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Some implications of the generalized Gauss-Bonnet theoremTransactions of the American Mathematical Society, 112
We get an explicit expression of curvature operators in terms of at most eight terms of sectional curvatures. Some applications of this result are also given, particularly we improve a result of Chen-Tian related to the first Chern class of admissible surfaces in pinched manifolds. We also characterize in a simple way all functionsk(x, y) which can be sectional curvatures of some curvature operatorR.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Feb 15, 2005
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