Homology Vanishing Theorems for Pinched Submanifolds
نویسندگان
چکیده
We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like mean curvature length second fundamental form. Homology vanishing results are given that strengthen sharpen previous ones. In addition, an integral bound is provided for Bochner operator compact Euclidean in terms Betti numbers.
منابع مشابه
Vanishing theorems for associative submanifolds
Let M7 a manifold with holonomy in G2, and Y 3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that MX,Y , the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner’s technique, we give a vanishing theorem that forces MX,Y to be locally smooth. MSC 2000: 53C38 (35J55, 53C21, 58J32).
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2022
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-022-01032-9