A Note on Nearly Sasakian and Nearly Cosymplictic Structures of 5-Dimensional Spheres

Nearly Integrable So(3) Structures on 5-dimensional Lie Groups

Recent work [5] on 5-dimensional Riemannian manifolds with an SO(3) structure prompts us to investigate which Lie groups admit such a geometry. The case in which the SO(3) structure admits a compatible connection with torsion is considered. This leads to a classification under special behaviour of the connection, which enables to recover all known examples, plus others bearing torsion of pure t...

Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

A note on nearly platonic graphs

We define a nearly platonic graph to be a finite k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for such a graph to have exactly one disparate face, and offer some conjectures, including the conjecture that nearly platonic graphs with two disparate faces come in a small set of families.

Nearly round spheres look convex

We prove that a Riemannian manifold (M, g), close enough to the round sphere in the C topology, has uniformly convex injectivity domains — so M appears uniformly convex in any exponential chart. The proof is based on the Ma–Trudinger–Wang nonlocal curvature tensor, which originates from the regularity theory of optimal transport.

Cr-submanifolds of a Nearly Trans-sasakian Manifold