7 citations · 17 across the 11 of their papers we have counts for
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On a special class of gradient Ricci solitons
José Nazareno Vieira Gomes, Marcus Antonio Mendonça Marrocos
We develop a method for constructing complete gradient Ricci solitons realized as fiber bundles endowed with warped metrics, and we establish necessary and sufficient conditions fo…
On the generic Simplicity of the spectrum for Connection Laplacian and -simplicity on Principal Bundles
Geovane C. Brito, Marcus A. M. Marrocos
In this paper, we prove that, for a residual set of connections defined on a smooth vector bundle , all eigenvalues of the connection Laplacian operator $\mathscr{…
Hidden symmetries and the generic spectral setting of generalized laplacians on homogeneous spaces
Diego S. De Oliveira, Marcus A. M. Marrocos
The purpose of this work is to establish the spectral setting of some generalized Laplace operators associated to a generic -invariant metric on a compact homogeneous space $M=G…
Hadamard-type variation formulae for the eigenvalues of a class of second-order elliptic operators and its applications
Cleiton Lira Cunha, José Nazareno Vieira Gomes, Marcus Antônio Mendonça Marrocos
We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold . We then apply the latter in t…
A note on gradient Ricci soliton warped metrics
José N. V. Gomes, Marcus A. M. Marrocos, Adrian V. C. Ribeiro
In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are real…
Generic spectrum of warped products and G-manifolds
Marcus A. M. Marrocos, José N. V. Gomes
In this paper, we establish a kind of splitting theorem for the eigenvalues of a specific family of operators on the base of a warped product. As a consequence, we prove a density…
On Eigenvalue Generic Properties of the Laplace-Neumann Operator
José N. V. Gomes, Marcus A. M. Marrocos
We establish the existence of analytic curves of eigenvalues for the Laplace-Neumann operator through an analytic variation of the metric of a compact Riemannian manifold with…