Topic
Linear complex structure
About: Linear complex structure is a research topic. Over the lifetime, 222 publications have been published within this topic receiving 4241 citations.
Papers published on a yearly basis
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Papers
TL;DR: A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations as mentioned in this paper, and a manifold can be called almost complex if there is a linear transformation J defined on the tangent space at every point, and varying differentiably with respect to local coordinates.
Abstract: A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations. On such a manifold scalar multiplication by i in the tangent space has an invariant meaning. An even dimensional 2n real manifold is called almost complex if there is a linear transformation J defined on the tangent space at every point (and varying differentiably with respect to local coordinates) whose square is minus the identity, i.e. if there is a real tensor field h' satisfying
869 citations
TL;DR: In this article, it was shown that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field.
Abstract: We prove that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a real hypersurface admitting so-called “$\eta$-Ricci soliton” in a non-flat complex space form.
245 citations
129 citations
TL;DR: An algorithm is presented that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of thecomplex in a consistent manner, providing a complete decomposition of the domain.
Abstract: The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.
119 citations
TL;DR: In this paper, the tangent bundle of a Lie groupoid G corresponds to the adjoint representation of G up to homotopy of G. The authors define a cochain complex that is canonically associated to any VB-groupoid and show that this complex is isomorphic to the groupoid cohomology with values in the corresponding representations.
Abstract: A VB-groupoid is a Lie groupoid equipped with a compatible linear structure. In this paper, we describe a correspondence, up to isomorphism, between VB-groupoids and 2-term representations up to homotopy of Lie groupoids. Under this correspondence, the tangent bundle of a Lie groupoid G corresponds to the "adjoint representation" of G. The value of this point of view is that the tangent bundle is canonical, whereas the adjoint representation is not.
We define a cochain complex that is canonically associated to any VB-groupoid. The cohomology of this complex is isomorphic to the groupoid cohomology with values in the corresponding representations up to homotopy. When applied to the tangent bundle of a Lie groupoid, this construction produces a canonical complex that computes the cohomology with values in the adjoint representation.
Finally, we give a classification of regular 2-term representations up to homotopy. By considering the adjoint representation, we find a new cohomological invariant associated to regular Lie groupoids.
79 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 2 |
| 2018 | 5 |
| 2017 | 7 |
| 2016 | 7 |