Harmonic and conformally Killing forms on complete Riemannian manifold
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 51-57
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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.
@article{IVM_2017_3_a4,
author = {S. E. Stepanov and I. I. Tsyganok and T. V. Dmitrieva},
title = {Harmonic and conformally {Killing} forms on complete {Riemannian} manifold},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {51--57},
publisher = {mathdoc},
number = {3},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2017_3_a4/}
}
TY - JOUR AU - S. E. Stepanov AU - I. I. Tsyganok AU - T. V. Dmitrieva TI - Harmonic and conformally Killing forms on complete Riemannian manifold JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2017 SP - 51 EP - 57 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2017_3_a4/ LA - ru ID - IVM_2017_3_a4 ER -
%0 Journal Article %A S. E. Stepanov %A I. I. Tsyganok %A T. V. Dmitrieva %T Harmonic and conformally Killing forms on complete Riemannian manifold %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2017 %P 51-57 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2017_3_a4/ %G ru %F IVM_2017_3_a4
S. E. Stepanov; I. I. Tsyganok; T. V. Dmitrieva. Harmonic and conformally Killing forms on complete Riemannian manifold. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 51-57. http://geodesic.mathdoc.fr/item/IVM_2017_3_a4/