Stable complex manifolds

Stable Complex Manifolds

1. T. Van de Ven [3] has recently shown that there exist real 4dimensional manifolds which admit almost complex structures but admit no complex structures, e.g. SXS* # SXS # CP(2). The purpose of this note is to show that this is an unstable phenomenon. Let M be a C w-dimensional real manifold without boundary and let TM be its tangent bundle. R is real Euclidean fe-space and C is complex &-spa...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Manifolds admitting stable forms

Special geometries defined by a class of differential forms on manifolds are again in the center of interests of geometers. These interests are motivated by the fact that such a setting of special geometries unifies many known geometries as symplectic geometry and geometries with special holonomy [Joyce2000], as well as other geometries arised in the M-theory [GMPW2004], [Tsimpis2005]. A series...

Complex Manifolds

is holomorphic. Thus P has the structure of a complex manifold, called complex projective space. The “coordinates” Z + [Z0, . . . , Zn] are called homogeneous coordinates on P. P is compact, since we have a continuous surjective map from the unit sphere in C to P. Note that P is just the Riemann sphere C ∪ {∞}. Any inclusion C → C induces an inclusion P → P; the image of such a map is called a ...