2024/12/19 by Leonardo Biliotti, Biliotti, Leonardo, Alessandro Minuzzo +1
Engineering · #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.2412.15424
Let Mi, for i=1,2, be a Kähler manifold, and let G be a Lie group acting on Mi by Kähler isometries. Suppose that the action admits a momentum map μi and let Ni:=μi-1(0) be a regular level set. When the action of G on Ni is proper and free, the Meyer--Marsden--Weinstein quotient Pi:=Ni/G is a Kähler manifold and πi:Ni→ Pi is a principal fiber bundle with base Pi and characteristic fiber G. In this paper, we define an almost complex structure for the manifold N1× N2 and give necessary and sufficient conditions for its integrability. In the integrable case, we find explicit holomorphic charts for N1× N2. As applications, we consider a non integrable almost-complex structure on the product of two complex Stiefel manifolds and the infinite Calabi-Eckmann manifolds \mathbb S2n+1× S(H), for n≥ 1, where S(H) denotes the unit sphere of an infinite dimensional Hilbert space H