Vector bundles over three-dimensional spherical space forms by Esdras Teixeira Costa, Oziride Manzoli Neto, Mauro Spreafico

“…We consider the problem of enumerating the G-bundles over low-dimensional manifolds (dimension ≤3) and in particular vector bundles over the three-dimensional spherical space forms. …”
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Une machine à tenseurs TT sur les variétés d’Einstein by Delay, Erwann

“…In all dimensions $n \ge 3$, we introduce a differential operator of order 4 which, on Einstein manifolds, transforms the (fields of) trace free symmetric two tensors into TT-tensors. …”
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On pz–Laplacian System Involving Critical Nonlinearities by Ahmed Aberqi, Jaouad Bennouna, Omar Benslimane, Maria Alessandra Ragusa

“…In this paper, we deal with the existence of at least two nonnegative nontrivial solutions to a pz–Laplacian system involving critical nonlinearity in the context of Sobolev spaces with variable exponents on complete manifolds. We have established our main results by exploring both Nehari’s method and doing a refined analysis on the associated fiber map and some variational techniques.…”
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Image sets of folding surfaces by Ana M. d'Azevedo Breda

“…Isometric foldings are a special class of length-preserving maps of Riemannian manifolds and were initially studied by S. Robertson. …”
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Regenerations and applications by Giovanni Mongardi, Gianluca Pacienza

“…We show that, for projective irreducible holomorphic symplectic manifolds, an analogous regeneration principle holds and provides a very flexible tool to prove existence of uniruled divisors, significantly improving known results.…”
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On the Electromagnetic Vacuum Origins of Dark Energy, Dark Matter, and Astrophysical Jets by Stuart Marongwe

“…We use a semiclassical version of the Nexus paradigm of quantum gravity in which the quantum vacuum at large scales is dominated by the second quantized electromagnetic field to demonstrate that a virtual photon field can affect the geometric evolution of Einstein manifolds or Ricci solitons. This phenomenon offers a cogent explanation of the origins of astrophysical jets, the cosmological constant, and a means of detecting galactic dark matter.…”
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Approximate Lie Symmetry Conditions of Autoparallels and Geodesics by Sameerah Jamal

“…Lastly, we exemplify the results by application to some approximate wave-like manifolds.…”
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Optimal $L^2$ Extensions of Openness Type and Related Topics by Xu, Wang, Zhou, Xiangyu

“…We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels. …”
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Notes on integrating out M2 branes by Jarod Hattab, Eran Palti

“…Abstract Integrating out supersymmetric M2 branes wrapped on two-cycles in Calabi–Yau manifolds is an important calculation: it allows the determination of, and in some ways defines, the free energy of topological strings. …”
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An application of stress energy tensor to the vanishing theorem of differential forms by Kairen Cai

“…It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p-form vanishes. …”
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Exact Computations in Topological Abelian Chern-Simons and BF Theories by Philippe Mathieu

“…We introduce Deligne cohomology that classifies U1 fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in U1 Chern-Simons theory (BF theory, resp.) at the level of functional integrals. …”
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Discrete Wilson Lines in F-Theory by Volker Braun

“…F-theory models are constructed where the 7 -brane has a nontrivial fundamental group. The base manifolds used are a toric Fano variety and a smooth toric threefold coming from a reflexive polyhedron. …”
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Gauged supergravity from the Lunin-Maldacena background by James T. Liu, Brian McPeak

“…We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution.…”
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On fuzzy subbundles of vector bundles by V. Murali, G. Lubczonok

“…We do these here with a view to introduce and study integrable fuzzy subbundles of tangent bundles on manifolds and foliations in further papers.…”
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Response of Immunotherapy to Tumour-TICLs Interactions: A Travelling Wave Analysis by Joseph Malinzi, Precious Sibanda, Hermane Mambili-Mamboundou

“…We use the geometric treatment of an apt-phase space to establish the intersection between stable and unstable manifolds. We calculate the minimum wave speed and numerical simulations are performed to support the analytical results.…”
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Vaclovas Bliznikas (1930–1997) – creator of Lithuanian geometers' school by Juozas Banionis

“…The main academic research activity embraced trends of modern geometry, theory of geometrical objects, geometry of differential equation, theory of non-holonomicity ma­nifolds, geometry of supporting elements. He published over 95 scientific articles in the scientific publications in Lithuania and East Europe, prepared 11 Doctors of Sciences, wrote 10 coursebooks for the students of high mathematics. …”
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BPS States, Crystals, and Matrices by Piotr Sułkowski

“…We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2- and D0-branes bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional D4-brane. …”
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Mirror symmetry for concavex vector bundles on projective spaces by Artur Elezi

“…Let X⊂Y be smooth, projective manifolds. Assume that ι:X→ℙs is the zero locus of a generic section of V+=⊕i∈I𝒪(ki), where all the ki's are positive. …”
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Auxiliary field deformations of (semi-)symmetric space sigma models by Daniele Bielli, Christian Ferko, Liam Smith, Gabriele Tartaglino-Mazzucchelli

“…Abstract We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in [1] and [2] to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. …”
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Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales by Xing Hu, Yongkun Li

“…Finally, as an application, by constructing an appropriate variational setting, using fibering mapping and Nehari manifolds, the existence of weak solutions for a class of fractional boundary value problems on time scales is studied, and a result of the existence of weak solutions for this problem is obtained.…”
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