Assignment Help - homework help

  Differential Geometry Homework Help - K-12 Grade Level, College Level Mathematics

Introduction to Differential Geometry

Differential geometry uses the methods of differential calculus and integral calculus, with the multi linear and linear algebra to study problems in geometry. The hypothesis of space and plane curves and of surfaces in the 3-dimensional Euclidean space created the basis for development of differential geometry during the 18th century and 19th century. As in the late 19th century, differential geometry has grown into a field concerned more usually with the geometric structures on differentiable manifolds. The differential geometry is closely related to differential topology and the geometric features of the theory of differential geometry s. The differential geometry of surfaces captures numerous key ideas and methods characteristic of this field.

1204_Differential Geometry Homework Help.jpg

Branches of differential geometry:

Riemannian geometry:

The Riemannian geometry studies smooth manifolds that are the Riemannian manifolds with a Riemannian metric. It is a notion of distance expressed by means of a smooth positive definite symmetric bilinear form defined on the tangent space at each point. It generalizes the Euclidean geometry to spaces that are not essentially flat, even though they resemble the Euclidean space at each infinite point that is in the initial order of approximation. Numerous concepts based on length, such as the area of arc length of curves, plane regions and volume of solids all possess natural analogues in Riemannian geometry. The concept of a directional derivative of a function from multivariable calculus is extended in Riemannian geometry to the notion of a covariant derivative of a tensor. Many methods and concepts of analysis and Differential geometry s have been generalized to the setting of Riemannian manifolds.

Pseudo-Riemannian Geometry:

The Pseudo-Riemannian geometry generalizes Riemannian geometry to the situation in which the metric tensor do not require to be positive-definite. The special case of this is a Lorentzian manifold that is the mathematical foundation of Einstein's general relativity theory of gravity.

Finsler Geometry:

Finsler geometry has the Finsler manifold as the main study object. It is a differential manifold with Finsler metric that is a Banach norm defined on each tangent space. A Finsler metric is a more common structure than a Riemannian metric. The Finsler structure on a manifold M is a function F: TM → [0, ∞) which is as follows:

1.)    F(x, my) = |m|F(x,y) for all x, y in TM

2.)    F is infinitely differentiable in TM - {0},

3.)    The vertical Hessian of F2 is positive definite.

Symplectic geometry:

The study of Symplectic manifolds is termed as Symplectic geometry. Almost all Symplectic manifold is a differentiable manifold prepared with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space which is a non degenerate 2-form ω which is known as the Symplectic form. The Symplectic manifold is almost Symplectic manifold for which the Symplectic form ω is closed i.e., dω = 0.

Contact geometry:

This kind of differential geometry deals with certain manifolds of odd dimension. It is closely associated to Symplectic geometry and like the later; it originated in questions of traditional mechanics.

CR geometry:

This kind of differential geometry is the study of the intrinsic geometry of boundaries of domains in the complex manifolds.

Email based Differential geometry Homework Help -Assignment Help

Tutors at the www.tutorsglobe.com are committed to provide the best quality Differential geometry homework help - assignment help. They use their experience, as they have solved thousands of the Differential geometry assignments, which may help you to solve your difficult Differential geometry homework. You can find solutions for all the topics come under the Complex analysis. The dedicated tutors provide eminence work on your Math homework help and devoted to provide K-12 level Math to college level Math help before the deadline mentioned by the student. Differential geometry homework help is available here for the students of school, college and university. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.

Qualified and Experienced Differential geometry Tutors at www.tutorsglobe.com

Tutors at the www.tutorsglobe.com take pledge to provide full satisfaction and assurance in Differential geometry homework help. Students are getting Math homework help services across the globe with 100% satisfaction. We value all our service-users. We provide email based Differential geometry homework help - assignment help. You can join us to ask queries 24x7 with live, experienced and qualified Math tutors specialized in Complex analysis.
Home | Company Overview | Services | Discover Q&A | Sitemap | Contact Us | T & C | Refund Policy | Copyright Policy | Blog | Q&A | Directory

©TutorsGlobe All rights reserved 2022-2023.