Positive curvature and symmetry in small dimensions
Positive curvature and symmetry in small dimensions
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DOI：
10.1142/s0219199719500536
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发表时间：
2019-06
影响因子：
1.6
通讯作者：
Manuel Amann;Lee Kennard
中科院分区：
文献类型：
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作者：
Manuel Amann;Lee Kennard
将已有的工作扩展到小维度，Dessai计算了[公式：见正文]-存在环面对称的正截曲率流形的欧拉特征、签名和椭圆亏格。他还通过将他的结果限制在已知允许非负曲率的流形类(如双商)来计算微分同胚型。本文的第一部分将Dessai的计算扩展到偶数维[公式：参见正文]。特别地，我们首次得到了在这种情况下的Cayley平面的特征。第二部分研究了一族密切相关的流形，称为正椭圆流形，并在此背景下证明了Halperin的一个猜想，其维度直到[公式：参见文本]或欧拉特征直到[公式：参见文本]。
Extending existing work in small dimensions, Dessai computed the Euler characteristic, signature, and elliptic genus for [Formula: see text]-manifolds of positive sectional curvature in the presence of torus symmetry. He also computes the diffeomorphism type by restricting his results to classes of manifolds known to admit non-negative curvature, such as biquotients. The first part of this paper extends Dessai’s calculations to even dimensions up to [Formula: see text]. In particular, we obtain a first characterization of the Cayley plane in such a setting. The second part studies a closely related family of manifolds called positively elliptic manifolds, and we prove a conjecture of Halperin in this context for dimensions up to [Formula: see text] or Euler characteristics up to [Formula: see text].