Geodesic
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/}
}
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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/