product of spherescomplex structurealmost complex Cayley structureoctave algebraIn this paper, we discuss almost complex structures on the sphere S6 and on the products of spheres S3 × S3, S1 × S5, and S2 × S4. We prove that all almost complex Cayley structures that naturally appear from ...
SYMPLECTIC AND COMPLEX GEOMETRIC ASPECTS OF THE 3-MANIFOLD EMBEDDING PROBLEM IN 热爱数学的小渣渣 30 0 ALMOST OPTIMAL PACKINGS OF EQUAL SPHERES IN DIMENSIONS 8 AND 24 热爱数学的小渣渣 9 0 John Conway Distinguished Lecture - The Symmetries of Things 热爱数学的小渣渣 50 0 [BOURBAKI 2021] Dan...
using obstruction theory and Yang's results on the existence of almost complex structures on (n-1)-connected 2n-manifolds. Finally, we partially extend Datta and Subramanian's result on the nonexistence of almost complex structures on products of two even spheres to rational homology spheres by ...
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Yano,Structures on Manifolds. Series in Pure Mathematics, Vol. 3 (1984). V. M. Miquel “Some examples of Riemannian almost-product manifolds,”Pacific J. Math.,111, No. 1, 163–178 (1984). MATH MathSciNet Google Scholar A. Montesinos, “Some integral invariants of plane fields on ...
This paper originates from the talk "Almost Complex Structures on Spheres" given by the second author at the MAM1 workshop "(Non)-existence of complex structures on S 6 S 6 mathContainer Loading Mathjax ", held in Marburg from March 27th to March 30th, 2017. It is a review paper, ...
Nonexistence of almost complex structures on products of even-dimensional spheresPrimary 53C15In this paper we prove the following theorem: S 2 p× S 2 q allows an almost complex structure if and only if ( p, q) = (1,1), (1,2), (2,1), (1,3), (3,1), (3,3).doi:10.1016/...
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere...
In this chapter we study the almost complex structures of a differentiable manifold. We give a definition in Sec. 1 and an example for the unit 6-sphereS6in Sec. 2. Section 3 contains a discussion of the complexification of a vector space over the set of all real numbers. In Sec. 4...
3-Sasakian geometryWe prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application, we provide several new examples of manifolds which admit taut contact circles, taut and round almost cosymplectic 2-spheres, and almost ...