Complex structures on tangent bundles of Riemannian manifolds

1991 ◽  
Vol 291 (1) ◽  
pp. 409-428 ◽  
Author(s):  
Róbert Szőke
Keyword(s):  
Riemannian Manifolds ◽  
Complex Structures ◽  
Tangent Bundles

HUMAN VERSUS HUMANOID ROBOT BIODYNAMICS

2008 ◽  
Vol 05 (04) ◽  
pp. 699-713 ◽  
Author(s):  
VLADIMIR G. IVANCEVIC ◽  
TIJANA T. IVANCEVIC
Keyword(s):  
Riemannian Manifolds ◽  
Humanoid Robot ◽  
Hamiltonian Dynamics ◽  
Human Motion ◽  
Cotangent Bundles ◽  
Human Joints ◽  
Configuration Manifolds ◽  
Compare And Contrast ◽  
Tangent Bundles ◽  
Validation Stage

In this paper we compare and contrast modern dynamical methodologies common to both humanoid robotics and human biomechanics. While the humanoid robot's motion is defined on the system of constrained rotational Lie groups SO(3) acting in all major robot joints, human motion is defined on the corresponding system of constrained Euclidean groups SE(3) of the full (rotational + translational) rigid motions acting in all synovial human joints. In both cases the smooth configuration manifolds, Q rob and Q hum , respectively, can be constructed. The autonomous Lagrangian dynamics are developed on the corresponding tangent bundles, TQ rob and TQ hum , respectively, which are themselves smooth Riemannian manifolds. Similarly, the autonomous Hamiltonian dynamics are developed on the corresponding cotangent bundles, T*Q rob and T*Q hum , respectively, which are themselves smooth symplectic manifolds. In this way a full rotational + translational biodynamics simulator has been created with 270 DOFs in total, called the Human Biodynamics Engine, which is currently in its validation stage. Finally, in both the human and the humanoid case, the time-dependent biodynamics generalizing the autonomous Lagrangian (of Hamiltonian) dynamics is naturally formulated in terms of jet manifolds.

scholarly journals Symplectic and Contact Geometry with Complex Manifolds

2019 ◽  
Vol 39 ◽  
pp. 119-126
Author(s):  
AKM Nazimuddin ◽  
Md Showkat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Contact Geometry ◽  
Symplectic Manifolds ◽  
Complex Structures ◽  
Contact Manifolds ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Real Submanifold ◽  
Complex Symplectic

In this paper, we discuss about almost complex structures and complex structures on Riemannian manifolds, symplectic manifolds and contact manifolds. We have also shown a special comparison between complex symplectic geometry and complex contact geometry. Also, the existence of a complex submanifold of n-dimensional complex manifold which intersects a real submanifold GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 119-126

On the tangent bundles of Finsler and Riemannian manifolds

1963 ◽  
Vol 12 (2) ◽  
pp. 211-228 ◽  
Author(s):  
K. Yano ◽  
E. T. Davies
Keyword(s):  
Riemannian Manifolds ◽  
Tangent Bundles

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
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