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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Scalar curvatures on $ O(M),G\sb{2}(M)$


Author: Alcibiades Rigas
Journal: Proc. Amer. Math. Soc. 61 (1976), 93-98
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1976-0425832-1
MathSciNet review: 0425832
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Abstract: We show that every $ {C^\infty }f:{G_2}(M) \to {\mathbf{R}},{M^n}$ a compact connected riemannian manifold $ n \geqslant 3$, is the scalar curvature function of some complete riemannian metric on $ {G_2}(M)$, the grassmann bundle of $ 2$ planes over $ M$, except possibly when $ K = {\text{constant }} \geqslant 0$. A similar result holds for $ O(M)$ bundle of orthonormal frames on $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0425832-1
Keywords: Riemannian metric, bundle of orthonormal frames, scalar and sectional curvature, grassmann $ 2$-plane bundle
Article copyright: © Copyright 1976 American Mathematical Society