Results 21 to 30 of about 95,625 (44)
A general Schwarz Lemma for almost-Hermitian manifolds
, 2007 We prove a version of Yau's Schwarz Lemma for general almost-complex manifolds equipped with Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem.
Tosatti, Valentino
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Almost Complex Structures on Homotopy Complex Projective Spaces [PDF]
arXiv, 2022 We show that all homotopy $\mathbb{C}P^n$s, smooth closed manifolds with the oriented homotopy type of $\mathbb{C}P^n$, admit almost complex structures for $3 \leq n \leq 6$, and classify these structures by their Chern classes. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on ...
arxiv
Constructing symplectic forms on 4-manifolds which vanish on circles
, 2004 Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles.
Gay, David T., Kirby, Robion
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The Square of Nijenhuis Tensor and Its Vanishing Results [PDF]
Asian-European Journal of Mathematics, Asian-European Journal of
Mathematics, volume 15, no 8(2022), 2020 We give the strong form and the weak form of the square of Nijenhuis tensor, and some vanish results of the square.
arxiv
On the Kodaira-Spencer's problem on almost Hermitian $4$-manifolds [PDF]
arXiv, 2023 In 1954, Hirzebruch reported a problem posed by Kodaira and Spencer: on compact almost complex manifolds, is the dimension $h^{p,q}_{\bar \partial}$ of the kernel of the Dolbeault Laplacian independent of the choice of almost Hermitian metric? In this paper, we review recent progresses on the original problem and we introduce a similar one: on compact ...
arxiv
Existence of foliations on 4-manifolds [PDF]
Algebr. Geom. Topol. 3 (2003) 1225-1256, 2003 We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures on most 4-manifolds. In certain cases, one can prescribe surfaces to be transverse or be leaves of these foliations.
arxiv +1 more source
On embeddings of almost complex manifolds in almost complex Euclidean spaces [PDF]
Journal of Geometry and Physics 101 (2016), 19-26, 2014 We prove that any compact almost complex manifold $(M, J)$ of real dimension $2m$ admits a pseudo-holomorphic embedding in a Euclidean space of dimension $4m + 2$, endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class of $(M, J)$, for the existence of
arxiv +1 more source
Mem. Amer. Math. Soc. 267 (2020), no. 1299, v+137, 2015 We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kaehler manifold gives rise to a c-projective structure and this is one of the primary motivations for ...
arxiv +1 more source
$C^{1,1}$ regularity of degenerate complex Monge-Ampère equations and some applications [PDF]
Analysis & PDE 14 (2021) 1671-1700, 2018 In this paper, we prove a $C^{1,1}$ estimate for solutions of complex Monge-Amp\`{e}re equations on compact almost Hermitian manifolds. Using this $C^{1,1}$ estimate, we show existence of $C^{1,1}$ solutions to the degenerate Monge-Amp\`{e}re equations, the corresponding Dirichlet problems and the singular Monge-Amp\`{e}re equations.
arxiv +1 more source
Geometry of universal embedding spaces for almost complex manifolds [PDF]
summary:We investigate the geometry of universal embedding spaces for compact almost-complex manifolds of a given dimension, and related constructions that allow for an extrinsic study of the integrability of almost-complex structures.
Clemente, Gabriella
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