Vanishing theorems for L2 harmonic 1-forms on complete submanifolds in a Riemannian manifold
- Authors
- Dung, Nguyen Thac; Seo, Keomkyo
- Issue Date
- Mar-2015
- Publisher
- Academic Press Inc.
- Keywords
- First eigenvalue; L2 harmonic 1-form; Traceless second fundamental form; δ-Stability inequality
- Citation
- Journal of Mathematical Analysis and Applications, v.423, no.2, pp 1594 - 1609
- Pages
- 16
- Journal Title
- Journal of Mathematical Analysis and Applications
- Volume
- 423
- Number
- 2
- Start Page
- 1594
- End Page
- 1609
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/10645
- DOI
- 10.1016/j.jmaa.2014.10.076
- ISSN
- 0022-247X
1096-0813
- Abstract
- Let M be an n-dimensional complete orientable noncompact hypersurface in a complete Riemannian manifold of nonnegative sectional curvature. For 2≤n≤6, we prove that if M satisfies the δ-stability inequality (0<δ≤1), then there is no nontrivial L2β harmonic 1-form on M for some constant β. We also provide sufficient conditions for complete hypersurfaces to satisfy the δ-stability inequality. Moreover, we prove a vanishing theorem for L2 harmonic 1-forms on M when M is an n-dimensional complete noncompact submanifold in a complete simply-connected Riemannian manifold N with sectional curvature KN satisfying that -k2≤KN≤0 for some constant k. © 2014 Elsevier Inc.
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