Higher Order Differential Geometry

1993 ◽  
pp. 115-168
Keyword(s):  
Differential Geometry ◽  
Higher Order

scholarly journals Generalizations and applications of Young’s integral inequality by higher order derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jun-Qing Wang ◽  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Differential Geometry ◽  
Integral Inequality ◽  
Higher Order ◽  
Integral Inequalities ◽  
List Type ◽  
Definite Integral ◽  
Exponential Integral ◽  
Definite Integrals ◽  
Logarithmic Integral

Abstract In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

scholarly journals Higher-Order Geodesic Equations from Non-Local Lagrangians and Complex Backward-Forward Derivative Operators

2016 ◽  
Vol 54 (1) ◽  
pp. 139-157
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Order Derivative ◽  
Lagrangian Dynamics ◽  
Derivative Operator ◽  
Geodesic Equations ◽  
Non Local ◽  
Extended Complex

Abstract Starting with an extended complex backwardforward derivative operator in differential geometry which is motivated from non-local-in-time Lagrangian dynamics, higher-order geodesic equations are obtained within classical differential geometrical settings. We limit our analysis up to the 2nd-order derivative where some applications are discussed and a number of features are revealed accordingly.

scholarly journals Differential geometry of higher order

Topology ◽  
1962 ◽  
Vol 1 (3) ◽  
pp. 169-211 ◽  
Author(s):  
William Francis Pohl
Keyword(s):  
Differential Geometry ◽  
Higher Order

scholarly journals Affine differential geometry of osculating hypersurfaces

2012 ◽  
Vol 53 ◽  
pp. 37-41
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Second Order ◽  
Affine Differential Geometry ◽  
Local Properties ◽  
Derivatives Of

Osculating surfaces of second order have been studied in classical affine differential geometry [1].  In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space. Various geometric interpretations are given. This yields a affinely invariant consideration of the local properties of a given hypersurface which depend on the derivatives of higher order.

scholarly journals Osculating surfaces of curves on surfaces

2020 ◽  
Vol 55 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Euclidean Space ◽  
Higher Order ◽  
Space Curves ◽  
Classical Differential Geometry ◽  
Surfaces In Euclidean Space ◽  
Curves On Surfaces

Oosculating sphere have been studied in classical differential geometry [1]. In this article the osculating surfaces of higher order of space curves on surfaces in Euclidean space is considered. We study the intrinsic differential geometry of curves  on surfaces by analyzing their contact with surfaces of higher order.

scholarly journals Osculating curves and surfaces

2012 ◽  
Vol 54 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Space Curves ◽  
Curves And Surfaces ◽  
Classical Differential Geometry

Osculating circle and osculating sphere have been studied in classical differential geometry [1]. In this article the osculating curves and surfaces of higher order of plane and space curves in Euclideann-space (n = 2, 3) is considered. We study the intrinsic differential geometry of curves by analyzing their contact with curves and surfaces of higher order.

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