On an Almost Complex Manifold Approach to Elementary Particles

1977 ◽  
Vol 32 (11) ◽  
pp. 1215-1221
Author(s):  
Julian Ławrynowicz ◽  
Leszek Wojtczak
Keyword(s):  
Complex Manifold ◽  
Nuclear Reactions ◽  
Main Idea ◽  
Elementary Particles ◽  
Fibre Bundles ◽  
Almost Complex Manifold ◽  
Minkowski Space Time ◽  
Almost Complex ◽  
Principal Fibre ◽  
Principal Fibre Bundles

Abstract An almost complex manifold description of elementary particles is proposed which links the approaches given independently by J. Ławrynowicz and L. Wojtczak, and by C. von Westenholz. This description leads to relations between the curvature form of an almost complex manifold, which accounts for the symmetry classification schemes within the frame of principal fibre bundles, and a curved Minkowski space-time via induced smooth mappings characterizing nuclear reactions of type N+π⇄N, where N is some nucleon and π the virtual π-meson of this reaction. Both approaches follow the same main idea of D. A. Wheeler developed in a different way by A.D. Sakharov.

scholarly journals On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action

2017 ◽  
Vol 19 (04) ◽  
pp. 1750043 ◽  
Author(s):  
Silvia Sabatini
Keyword(s):  
Fixed Points ◽  
Complex Manifold ◽  
Index Formula ◽  
Circle Action ◽  
Hilbert Polynomial ◽  
Dimensional Manifold ◽  
Hamiltonian Action ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Chern Numbers

Let [Formula: see text] be a compact, connected, almost complex manifold of dimension [Formula: see text] endowed with a [Formula: see text]-preserving circle action with isolated fixed points. In this paper, we analyze the “geography problem” for such manifolds, deriving equations relating the Chern numbers to the index [Formula: see text] of [Formula: see text]. We study the symmetries and zeros of the Hilbert polynomial, which imply many rigidity results for the Chern numbers when [Formula: see text]. We apply these results to the category of compact, connected symplectic manifolds. A long-standing question posed by McDuff and Salamon asked about the existence of non-Hamiltonian actions with isolated fixed points. This question was answered recently by Tolman, with an explicit construction of a 6-dimensional manifold with such an action. One issue that this raises is whether one can find topological criteria that ensure the manifold can only support a Hamiltonian or only a non-Hamiltonian action. In this vein, we are able to deduce such criteria from our rigidity theorems in terms of relatively few Chern numbers, depending on the index. Another consequence is that, if the action is Hamiltonian, the minimal Chern number coincides with the index and is at most [Formula: see text].

scholarly journals Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds

2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Lorenzo Sillari ◽  
Adriano Tomassini
Keyword(s):  
Complex Manifold ◽  
Sufficient Condition ◽  
Complex Manifolds ◽  
Necessary And Sufficient Condition ◽  
Dolbeault Cohomology ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Necessary And Sufficient

AbstractIn this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.

Normal Variations of Invariant Hypersurfaces of Framed Manifolds

1972 ◽  
Vol 15 (4) ◽  
pp. 513-521
Author(s):  
Samuel I. Goldberg
Keyword(s):  
Complex Manifold ◽  
Contact Structure ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Marked Contrast ◽  
Almost Complex Manifold ◽  
Almost Contact Structure ◽  
Almost Complex ◽  
Differentiable Vector ◽  
Real Codimension

A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.

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