Composite optimization problems on Riemannian manifolds pose a unique computational challenge due to the non-Euclidean geometry of the manifold. In such problems, the objective function is composed of several terms defined on the Riemannian manifold, which requires specialized optimization techniques that ...
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They are significant elements in the study of the geometry of various types of manifolds. A smooth vector field P on a semi-Riemannian manifold (𝑁,ℎ)(N,h) is termed a conformal vector field if its flow results in conformal transformations or, equivalently, if the Lie derivative £...
Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic * Author to whom correspondence should be addressed. Mathematics 2022, 10(1), 154; https://doi.org/10.3390/math10010154 Submission received: 14 December 2021 / Revised: 24 December 2021...
Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research ...
Such a transformation is calleda concircular transformationin 𝑅𝑁, andconcircular geometryis geometry that treats the concircular transformations and the spaces that allow such kinds of transformations. In the 𝐺𝑅𝑁, we consider transformations 𝑔¯𝑖𝑗=𝜌2𝑔𝑖𝑗,(𝑔𝑖...
The geometry of these manifolds is largely determined by the presence of a pair of B-metrics that are related each other by the almost-contact structure. Recall that the conformal class of the metric is preserved by the Yamabe flow. With this reason in mind, we study Yamabe solitons and ...