“…Using Bochner's methods (see Stepanov [49]), Tachibana and Ishihara [50,51], Hasegawa and Yamauchi [52], and Akbar-Zadeh and Couty [53,54] also discovered new results. Later, Sinyukov [55] and Mikeš [10,56] also continued this research.…”
In this work, we consider holomorphically projective mappings of (pseudo-) Kähler spaces. We determine the conditions for finite complete geodesics that must be satisfied for the mappings to be trivial; i.e., these spaces are rigid.
“…Using Bochner's methods (see Stepanov [49]), Tachibana and Ishihara [50,51], Hasegawa and Yamauchi [52], and Akbar-Zadeh and Couty [53,54] also discovered new results. Later, Sinyukov [55] and Mikeš [10,56] also continued this research.…”
In this work, we consider holomorphically projective mappings of (pseudo-) Kähler spaces. We determine the conditions for finite complete geodesics that must be satisfied for the mappings to be trivial; i.e., these spaces are rigid.
In this survey, we consider one aspect of the Bochner technique, the proof of vanishing theorems by using the Weitzenbock integral formulas, which allows us to extend the technique to pseudo-Riemannian manifolds and equiaffine connection manifolds.
We prove in this paper a divergence theorem for symmetric ð0; 2Þ-tensors on a semi-Riemannian manifold with boundary. We obtain a generalization of results obtained by U ¨nal in [9, Acta Appl. Math. 40(1995)] and E. Garcı ´a-Rı ´o and D. N. Kupeli in [4,
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