ﻻ يوجد ملخص باللغة العربية
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian as an ordinary differential equation. Our method is based on a moment map technique and the classification of cohomogeneity one actions on the complex projective space classified by Takagi.
The aim of this paper is to classify cohomogeneity one isometric actions on the 4-dimensional Minkowski space $mathbb{R}^{3,1}$, up to orbit equivalence. Representations, up to conjugacy, of the acting groups in $O(3,1)ltimes mathbb{R}^{3,1}$ are giv
We prove the hypersymplectic flow of simple type on standard torus $mathbb{T}^4$ exists for all time and converges to the standard flat structure modulo diffeomorphisms. This result in particular gives the first example of a cohomogeneity-one $G_2$-L
We prove a conjecture formulated by Pablo M. Chacon and Guillermo A. Lobos in [Pseudo-parallel Lagrangian submanifolds in complex space forms, Differential Geom. Appl.] stating that every Lagrangian pseudo-parallel submanifold of a complex space form of dimension at least 3 is semi-parallel.
In this paper, we prove that principal circle bundles over the complex projective space equipped with the standard Sasakian structures are volume rigid among all $K$-contact manifolds satisfying positivity conditions of tensors involing the Tanaka-Webster curvature.
We exhibit the first examples of closed 4-manifolds with nonnegative sectional curvature that lose this property when evolved via Ricci flow.