Geometry of the second-order tangent bundles of Riemannian manifolds

2017 ◽  
Vol 38 (4) ◽  
pp. 985-998 ◽  
Author(s):  
Aydin Gezer ◽  
Abdullah Magden
Keyword(s):  
Riemannian Manifolds ◽  
Second Order ◽  
Tangent Bundles ◽  
Order Tangent

scholarly journals Second order tangent bundles of infinite dimensional manifolds

2004 ◽  
Vol 52 (2) ◽  
pp. 127-136 ◽  
Author(s):  
C.T.J. Dodson ◽  
G.N. Galanis
Keyword(s):  
Second Order ◽  
Infinite Dimensional ◽  
Tangent Bundles ◽  
Order Tangent

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Canonical Poisson–Nijenhuis structures on higher order tangent bundles

2014 ◽  
Vol 111 (1) ◽  
pp. 21-37
Author(s):  
P. M. Kouotchop Wamba
Keyword(s):  
Higher Order ◽  
Tangent Bundles ◽  
Order Tangent

scholarly journals Geometric Dynamics on Riemannian Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 79 ◽  
Author(s):  
Constantin Udriste ◽  
Ionel Tevy
Keyword(s):  
Differential Equations ◽  
Riemannian Manifolds ◽  
Riemannian Metrics ◽  
Second Order ◽  
Time Dynamics ◽  
Outer Planets ◽  
Time Motion ◽  
Euclidean Metrics ◽  
Economical System ◽  
Geometric Dynamics

The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m-distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.

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