Analysis on Differentiable Manifolds
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".
Deadline for manuscript submissions: 20 August 2025 | Viewed by 431
Special Issue Editor
Interests: Ricci-Bourguignon solitons; statistical manifolds; polynomial structures and affine connections in generalized geometry; warped product and slant submanifolds; magnetic and biharmonic curves and surfaces; multisymplectic structures
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Special Issue Information
Dear Colleagues,
An important problem in submanifold theory consists of finding optimal inequalities which relate extrinsic to intrinsic invariants for submanifolds in different ambient manifolds (endowed with polynomial structures and affine connections). Such invariants and inequalities have many applications in several areas of mathematics and related sciences. Minimal surfaces are known to be good mathematical models for physical phenomena, having been intensively studied in general relativity (black holes), cell biology (the endoplasmic reticulum), soap films, and materials science.
Geometric flows on (pseudo-)Riemannian manifolds are usually associated with extrinsic or intrinsic curvatures. One of the most studied flows is the Ricci flow introduced by Hamilton, whose self-similar solutions are Ricci solitons, which constitute natural generalizations of Einstein metrics. Another generalization of Einstein manifolds is the quasi-Einstein manifolds, important in the general theory of relativity, e.g., Robertson–Walker spacetime.
This Special Issue aims to collect reviews or research papers on topics concerning the geometry and topology of manifolds and submanifolds, as well as applications in mathematics or other scientific areas. Such topics can include, but are not limited to the following: manifolds with polynomial structures, (pseudo-)Riemannian metrics, and affine connections; distributions, foliations, and submanifolds; distinguished vector fields, vector bundles, and fiber bundles; geometric flows and solitons; spacetimes, etc.
Dr. Adara M. Blaga
Guest Editor
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Keywords
- differentiable manifold
- (pseudo-)Riemannian metric
- submanifold
- curvature
- optimal inequalities
- affine connection
- polynomial structure
- quasi-Einstein manifold
- spacetime
- geometric flow
- soliton
- vector field
- fiber bundle
- vector distribution
- foliations
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