2 citations · 3 across the 13 of their papers we have counts for
14 papers
On the embeddability of the homogeneous Ricci flow and its collapses
Mauro Patrão, Lucas Seco, Llohann D. Sperança
This article grew out of the urge to realize explicit examples of solutions for the Ricci flow as families of isometrically embedded submanifolds, together with its Gromov-Hausdorf…
The curvature of convex sum of metrics and applications
Leonardo F. Cavenaghi, Giovane Galindo, Llohann D. Sperança
In this note, we derive explicit formulae for the curvature of a convex sum of Riemannian metrics, \(g_t = (1-t)g_0 + t g_1\). We study whether such a deformation can increase the…
The -equivariant Kazdan--Warner problem
Leonardo F. Cavenaghi, João Marcos do Ó, Llohann D. Sperança
We establish an equivariant analogue of the Kazdan--Warner trichotomy for admissible scalar curvature functions. Let be a closed connected manifold of dimension equip…
A direct approach to prescribing scalar curvature on bundles
Leonardo Francisco Cavenaghi, Llohann Dallagnol Sperança
This note intends to demonstrate how to discuss scalar curvature functions' admissibility on bundles by directly applying some of the Kazdan--Warner results. Proofs of the concept…
On the completeness of dual foliations on nonnegatively curved symmetric spaces
Renato J. M. e Silva, Llohann D. Sperança
We prove Wilking's Conjecture about the completeness of dual leaves for the case of Riemannian foliations on nonnegatively curved symmetric spaces. Moreover, we conclude that such…
The projected homogeneous Ricci flow and three-isotropy-summands flag manifolds
Lino Grama, Ricardo M. Martins, Mauro Patrão +2
The Ricci flow was introduced by Hamilton and gained its importance through the years. Of special importance is the limiting behavior of the flow and its symmetry properties. Takin…
Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0
Vladimir Blinovsky, Llohann D. Sperança, Alexander Pchelintsev
Assuming that Brouwers Conjecture the upper bound for the sum of t< n largest eigenvalues of Laplacian graph on n vertices true for n <n_0, we prove the Brouwers Conjecture BC for…
Metric Foliations on the Euclidean Space
Llohann D. Sperança, Steffen Weil
We complete a minor gap in Gromoll and Walschap classification of metric fibrations from the Euclidean space, thus completing the classification of Riemannian foliations on Euclide…
An intrinsic curvature condition for submersions over Riemannian manifolds
Llohann D. Sperança
Let be a submersion equipped with a horizontal connection over a Riemannian manifold . We present an intrinsic curvature condition…
Totally Geodesic Riemannian Foliations on Compact Lie Groups
Llohann D. Sperança
In 86, Ranjan questioned whether a submersion from a compact simple Lie group with bi-invariant metric is a coset foliation or not, provided the submersion is Riemannia…
On Riemannian Foliations over Positively Curved Manifolds
Llohann D. Sperança
We prove that, under reasonable conditions, odd co-dimension Riemannian foliations cannot occur in positively curved manifolds.
Flat Sections and Non-negative Curvature in Pullback Bundles
C. Durán, L. D. Sperança
We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of…
An obstructions to Non-negative curvature on Bundles with Pull-back connections
Llohann Sperança
Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian…
Pulling back the Gromoll-Meyer construction and models of exotic spheres
Llohann D. Sperança
Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spher…