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pro vyhledávání: '"Cavenaghi, Leonardo"'
In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning provided by
Externí odkaz:
http://arxiv.org/abs/2405.07322
This paper investigates the nature of exotic spheres from two novel perspectives, addressing the fundamental question: ``What makes an exotic sphere exotic?'' First, we explore spherical T-duality in the context of $\mathrm{S}^3$-bundles over $\mathr
Externí odkaz:
http://arxiv.org/abs/2404.19088
Autor:
Cavenaghi, Leonardo F., Grama, Lino
Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a smooth stru
Externí odkaz:
http://arxiv.org/abs/2403.08960
This paper explores the existence and properties of \emph{basic} eigenvalues and eigenfunctions associated with the Riemannian Laplacian on closed, connected Riemannian manifolds featuring an effective isometric action by a compact Lie group. Our pri
Externí odkaz:
http://arxiv.org/abs/2402.10106
A singular foliation $\mathcal{F}$ on a complete Riemannian manifold $M$ is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of $M$ into orbits of an isometric action. In this paper, we i
Externí odkaz:
http://arxiv.org/abs/2311.07058
The family of invariant Riemannian manifolds in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$ is described by three parameters $(x,y,z)$ of positive real numbers. By restricting such a family of metrics in the \emph{tetrahedron} $\cal{T}:=
Externí odkaz:
http://arxiv.org/abs/2307.06418
In this note, we show that the classical Wallach manifold $\mathrm{SU}(3)/\mathrm{T}^2$-admits metrics of positive intermediate Ricci curvature $(\mathrm{Ric}_d >0)$ for $d = 1, 2, 3, 4, 5$ that lose these properties under the homogeneous Ricci flow
Externí odkaz:
http://arxiv.org/abs/2305.06119
We realize specific classical symmetric spaces, like the semi-K\"ahler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and Lagrangian
Externí odkaz:
http://arxiv.org/abs/2302.09638
Autor:
Cavenaghi, Leonardo F., Grama, Lino
The motivation for this work stems from the authors' desire to revive the study of ``fat bundles''. Recently, several new works have emerged in this field, including \cite{DV2022, cavenaghilinollohann2, ovando1, ovando2, BOCHENSKI2016131}, while the
Externí odkaz:
http://arxiv.org/abs/2212.08154
Autor:
Cavenaghi, Leonardo F.
In his unpublished notes on fat bundles, W. Ziller poses a compelling question: given a fat principal $G$-bundle $(P, g) \rightarrow (B, h)$ with $\dim G = 3$, and $g$ representing a Riemannian submersion metric ensuring that the $G$-orbits are total
Externí odkaz:
http://arxiv.org/abs/2207.10757