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| On the Generalized Geroch Conjecture for Complete Spin Manifolds* |
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Citation： |
Xiangsheng WANG,Weiping ZHANG.On the Generalized Geroch Conjecture for Complete Spin Manifolds*[J].Chinese Annals of Mathematics B,2022,43(6):1143~1146 |
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Net amount： 640 |
Authors： |
Xiangsheng WANG; Weiping ZHANG |
Foundation： |
National Natural Science Foundation of China (Nos. 11931007,12101361), the Nankai Zhide Foundation, the project of Young Scholars of SDU and the Fundamental Research Funds of SDU (No. 2020GN063). |
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| Abstract： |
Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold, the authors show that the connected sum M#W admits no complete metric of positive scalar curvature. When W = Tn, this provides a positive answer to the generalized Geroch conjecture in the spin setting. |
Keywords： |
Positive scalar curvature, Connected sum, Spin manifolds |
Classification： |
58J20, 53C21 |
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