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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 3, Pages 51–57 (Mi ivm9216)  

Harmonic and conformally Killing forms on complete Riemannian manifold

S. E. Stepanova, I. I. Tsyganoka, T. V. Dmitrievab

a 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00756_a
16-01-00053_a


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

Bibliographic databases:

UDC: 514.764
Received: 13.09.2015

Citation: S. E. Stepanov, I. I. Tsyganok, T. V. Dmitrieva, “Harmonic and conformally Killing forms on complete Riemannian manifold”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 3, 51–57; Russian Math. (Iz. VUZ), 61:3 (2017), 44–48

Citation in format AMSBIB
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\by S.~E.~Stepanov, I.~I.~Tsyganok, T.~V.~Dmitrieva
\paper Harmonic and conformally Killing forms on complete Riemannian manifold
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 3
\pages 51--57
\mathnet{http://mi.mathnet.ru/ivm9216}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 3
\pages 44--48
\crossref{https://doi.org/10.3103/S1066369X17030057}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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