Closed Geodesics on Weingarten Surfaces with

FE Baginski, VR Batista - SIAM Journal on Applied Dynamical Systems, 2024 - SIAM
In 2006, Alexander proved a result that implies for a Weingarten surface, if is the number of
times a closed geodesic winds around the axis of rotation and is the number of times the …

Mechanics of incompressible test bodies moving on λ‐spheres.

V Kovalchuk, I Mladenov - Mathematical Methods in the …, 2022 - search.ebscohost.com
The considerations of the mechanics of incompressible test bodies moving on spheres are
generalized to the case of λ‐spheres. Both surfaces are examples of Riemannian manifolds …

λ‐spheres as a new reference model for the geoid

V Kovalchuk, IM Mladenov - Mathematical Methods in the …, 2023 - Wiley Online Library
We propose here a new reference model approximating the actual shape of the Earth. It is
based on λ λ‐spheres as an alternative to the rotational ellipsoids. Relying on quite …

Mylar balloon and associated geometro-mechanical moments

V Kovalchuk, VI Pulov, IM Mladenov - Mathematics, 2023 - mdpi.com
Starting with identifications of the very fundamental geometric characteristics of a Mylar
balloon such as the profile curve, height, volume, arclength, surface area, crimping factor …

Geometry of Enumerable Class of Surfaces Associated with Mylar Balloons

VI Pulov, V Kovalchuk, IM Mladenov - Mathematics, 2024 - mdpi.com
In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the
profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as …

Closed Geodesics on the Mylar Balloon Shape

F Baginski, VR Batista - The American Mathematical Monthly, 2024 - Taylor & Francis
In 2006, Alexander proved a result that implied for the mylar balloon shape, if n is the
number of times a closed geodesic winds around the axis of rotation and m is the number of …

Unifying approach to Heisenberg models for spin distributions on curved surfaces of revolution with isothermal (conformal) metrics

V Kovalchuk, P Chudziński - Mathematical Methods in the …, 2023 - Wiley Online Library
In the present article, a unifying approach to description of different Heisenberg models (ie,
XY model, isotropic case, easy‐plane, and easy‐axis regimes) for spin distributions on …

Torus-Like Balloons

IM Mladenov - 2020 - projecteuclid.org
The concepts for inflatable deployable structures have been under development and
evaluation for many years. Strangely enough only the Mylar balloon up to now has been …