This article is cited in 1 paper

Harmonic and conformally Killing forms on complete Riemannian manifold

S. E. Stepanov^a, I. I. Tsyganok^a, T. V. Dmitrieva<sup>b

a</sup> Financial University at the Government of the Russian Federation, 49–55 Leningradskii Ave., Moscow, 125993 Russia
^b Russian State Social University, 4 Wilhelm Pieck str., Bld. 1, Moscow, 129226, Russia

Abstract: We present a classification of complete locally irreducible Riemannian manifolds with nonnegative curvature operator, which admit a nonzero and nondecomposable harmonic form with its square-integrable norm. We prove a vanishing theorem for harmonic forms on complete generic Riemannian manifolds with nonnegative curvature operator. We obtain similar results for closed and co-closed conformal Killing forms.

Keywords: complete Riemannian manifold, curvature operator, harmonic forms, conformal Killing forms, classification theorem, vanishing theorem.

UDC: 514.764

Received: 13.09.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:3, 44–48

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