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Results Concerning Almost Complex Structures on the Six-Sphere
Scott O. Wilson Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Queens, NY 11367, USA
Аннотация:
For the standard metric on the six-dimensional sphere, with Levi-Civita connection $\nabla$, we show there is no almost complex structure $J$ such that $\nabla_X J$ and $\nabla_{JX} J$ commute for every $X$, nor is there any integrable $J$ such that $\nabla_{JX} J = J \nabla_X J$ for every $X$. The latter statement generalizes a previously known result on the non-existence of integrable orthogonal almost complex structures on the six-sphere. Both statements have refined versions, expressed as intrinsic first order differential inequalities depending only on $J$ and the metric. The new techniques employed include an almost-complex analogue of the Gauss map, defined for any almost complex manifold in Euclidean space.
Ключевые слова:
six-sphere; almost complex; integrable.
Поступила: 20 ноября 2017 г.; в окончательном варианте 9 апреля 2018 г.; опубликована 17 апреля 2018 г.
Образец цитирования:
Scott O. Wilson, “Results Concerning Almost Complex Structures on the Six-Sphere”, SIGMA, 14 (2018), 034, 21 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1333 https://www.mathnet.ru/rus/sigma/v14/p34
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