scholarly journals Metric Tensor and Christoffel Symbols Based 3D Object Categorization

2015 ◽  
pp. 138-151
Author(s):  
Syed Altaf Ganihar ◽  
Shreyas Joshi ◽  
Shankar Setty ◽  
Uma Mudenagudi
Keyword(s):  
Object Categorization ◽  
Metric Tensor ◽  
3D Object ◽  
Christoffel Symbols

scholarly journals Metric tensor and Christoffel symbols based 3D object categorization

2014 ◽  
Author(s):  
Syed Altaf Ganihar ◽  
Shreyas Joshi ◽  
Shankar Shetty ◽  
Uma Mudenagudi
Keyword(s):  
Object Categorization ◽  
Metric Tensor ◽  
3D Object ◽  
Christoffel Symbols

PointDCCNet: 3D Object Categorization Network using Point Cloud Decomposition

2021 ◽  
Author(s):  
Siddharth Katageri ◽  
Sameer Kulmi ◽  
Ramesh Ashok Tabib ◽  
Uma Mudenagudi
Keyword(s):  
Point Cloud ◽  
Object Categorization ◽  
3D Object

Metric Spaces and Geodesic Motion

2019 ◽  
pp. 355-384
Author(s):  
David D. Nolte
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Parallel Transport ◽  
Variational Calculus ◽  
Geodesic Equation ◽  
Geodesic Curve ◽  
Geodesic Motion ◽  
Metric Tensor ◽  
Christoffel Symbols ◽  
Derivatives Of

The metric tensor uniquely defines the geometric properties of a metric space, while differential geometry is concerned with the derivatives of vectors and tensors within the metric space. Derivatives of vector quantities include the derivatives of basis vectors, which lead to Christoffel symbols that are directly connected to the metric tensor. This connection between tensor derivatives and the metric tensor provides the tools necessary to define geodesic curves. The geodesic equation is derived from variational calculus and from parallel transport. Geodesic motion is the trajectory of a particle through a metric space defined by an action metric that includes a potential function. In this way, dynamics converts to geometry as a trajectory in a potential converts to a geodesic curve through an appropriately defined metric space.

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