Results 41 to 50 of about 250 (140)

Harmonic tori in quaternionic projective 3-spaces [PDF]

Proceedings of the American Mathematical Society, 1997
Summary: Burstall classified conformal non-superminimal harmonic two-tori in spheres and complex projective spaces. In this paper, we classify conformal non-superminimal harmonic two-tori in a 2- or 3-dimensional quaternionic projective space, which are not always covered by primitive harmonic two-tori of finite type.
openaire   +2 more sources

Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3634-3642, December 2024.
Abstract We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank‐one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex‐valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple ...
F. E. Burstall
wiley   +1 more source

Zero‐curvature subconformal structures and dispersionless integrability in dimension five

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract We extend the recent paradigm “Integrability via Geometry” from dimensions 3 and 4 to higher dimensions, relating dispersionless integrability of partial differential equations to curvature constraints of the background geometry. We observe that in higher dimensions on any solution manifold, the symbol defines a vector distribution equipped ...
Boris Kruglikov, Omid Makhmali
wiley   +1 more source

Metrics of positive Ricci curvature on simply‐connected manifolds of dimension 6k$6k$

Journal of Topology, Volume 17, Issue 4, December 2024.
Abstract A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply‐connected 6‐manifold admits a Riemannian metric of positive scalar curvature. For metrics of positive Ricci curvature, it is widely open whether a similar result holds; there are no obstructions known for those manifolds to admit a metric of positive Ricci ...
Philipp Reiser
wiley   +1 more source

Heavenly metrics, hyper‐Lagrangians and Joyce structures

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract In [Proc. Sympos. Pure Math., American Mathematical Society, Providence, RI, 2021, pp. 1–66], Bridgeland defined a geometric structure, named a Joyce structure, conjectured to exist on the space M$M$ of stability conditions of a CY3$CY_3$ triangulated category.
Maciej Dunajski, Timothy Moy
wiley   +1 more source

Multiplicative generalized tube surfaces with multiplicative quaternions algebra

Mathematical Methods in the Applied Sciences, Volume 47, Issue 11, Page 9157-9168, 30 July 2024.
Along with other types of calculus, multiplicative calculus brings an entirely new perspective. Geometry now has a new field as a result of this new understanding. In this study, multiplicative differential geometry was used to explore peculiar surfaces. Multiplicative quaternions are also used to depict surfaces.
Hazal Ceyhan, Zehra Özdemir, Ismail Gök   +2 more
wiley   +1 more source

Hofer–Zehnder capacity of disc tangent bundles of projective spaces

Journal of the London Mathematical Society, Volume 110, Issue 1, July 2024.
Abstract We compute the Hofer–Zehnder capacity of disc tangent bundles of the complex and real projective spaces of any dimension. The disc bundle is taken with respect to the Fubini–Study resp. round metric, but we can obtain explicit bounds for any other metric.
Johanna Bimmermann
wiley   +1 more source

Closed 3‐forms in five dimensions and embedding problems

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
wiley   +1 more source

Totally Real Submanifolds in a Quaternion Projective Space

Tokyo Journal of Mathematics, 1996
Let \(M\) be an \(n\)-dimensional compact totally real minimal submanifold in the quaternionic projective space \(QP^n(c)\) of constant quaternionic sectional curvature \(c\). Denote by \(\rho\) the scalar curvature of \(M\), by \(\sigma\) the second fundamental form of \(M\), and by \(K_c\) and \(Q\) the functions assigning to each point \(p\in M ...
openaire   +4 more sources

Brane structures in microlocal sheaf theory

Journal of Topology, Volume 17, Issue 1, March 2024.
Abstract Let L$L$ be an exact Lagrangian submanifold of a cotangent bundle T∗M$T^* M$, asymptotic to a Legendrian submanifold Λ⊂T∞M$\Lambda \subset T^{\infty } M$. We study a locally constant sheaf of ∞$\infty$‐categories on L$L$, called the sheaf of brane structures or BraneL$\mathrm{Brane}_L$.
Xin Jin, David Treumann
wiley   +1 more source