Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature

Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature

In this paper, we show several vanishing theorems for harmonic p -forms on compact manifolds, and L q harmonic p -forms on complete noncompact manifolds with nonnegative scalar curvature, under various pointwise or integral curvature conditions. These conditions involve the positive Yamabe invariant...

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Veröffentlicht in:Geometriae dedicata 2019-08, Vol.201 (1), p.187-201
1. Verfasser: Lin, Hezi
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Curvature
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Riemann manifold
Tensors
Theorems
Topology
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Beschreibung
Zusammenfassung:In this paper, we show several vanishing theorems for harmonic p -forms on compact manifolds, and L q harmonic p -forms on complete noncompact manifolds with nonnegative scalar curvature, under various pointwise or integral curvature conditions. These conditions involve the positive Yamabe invariant, the weighted Poincaré inequality and the pure curvature tensor.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-018-0388-4