<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 2<italic><sup>nd</sup></italic>-order derivative where some applications are discussed and a number of features are revealed accordingly.</p></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.

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

Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671, Athens,

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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 from Non-Local Lagrangians and Complex Backward-Forward Derivative Operators

Published Online: Sep 24, 2016

Page range: 139 - 157

Received: Feb 07, 2016

Accepted: May 16, 2016

DOI: https://doi.org/10.1515/awutm-2016-0008

Keywords
Non-local-in-time Lagrangians, Extended complex backward-forward derivative operator, higher-order geodesic equations, higher-order geodesic deviation equations, complexified metric

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 24, 2016

Page range: 139 - 157

Received: Feb 07, 2016

Accepted: May 16, 2016

DOI: https://doi.org/10.1515/awutm-2016-0008

KeywordsNon-local-in-time Lagrangians, Extended complex backward-forward derivative operator, higher-order geodesic equations, higher-order geodesic deviation equations, complexified metric

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Non-local-in-time Lagrangians, Extended complex backward-forward derivative operator, higher-order geodesic equations, higher-order geodesic deviation equations, complexified metric