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, ...
(metric) structures. These examples generalize the well-known examples of contact circles defined by the Liouville-Cartan forms on the unit cotangent bundle of Riemann surfaces. Further, we provide sufficient conditions for a compact complex contact manifold to be the twistor space of a positive ...
S. E. Stepanov, “On one class of Riemannian almost product structures,”Izv. Vuzov, Mat., No. 7, 40–46 (1989). Google Scholar R. Akhil, “Structural equations and integral formula for foliated manifolds,”Geom. Dedic.,20, 85–91 (1986). ...
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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/...
Almost complex structures on S2 - McDuff () Citation Context ...3.2 for Xλ ⊂ Jλ. Replacing holomorphic spheres by pseudo-holomorphic ones, and complex deformation theory by gluing techniques for pseudo-holomorphic spheres, one can prove the following theorem (see =-=[M]-=-). Theorem ...
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-s...
robinson structures are lorentzian analogues of (almost) hermitian structures, to borrow the expression from nurowski and trautman [ 63 ]. in both cases, the underlying geometric object is that of an almost null structure , that is, a totally null complex \((m+1)\) -plane distribution. ...
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 ...
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 ...