Question: If w is a (k- 1) -form on a compact k-dimensional manifold M, prove that Mdw =0. Give a counter-example if M is not compact.

If w is a (k- 1) -form on a compact k-dimensional manifold M, prove that ∫Mdw =0. Give a counter-example if M is not compact.

Step by Step Solution

★★★★★

3.48 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

One has as is emp... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

M-C (97).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Verify that if W is a subspace of an inner product space V and v is in V, then perpw (v) is orthogonal to all w in W.

Q:

Show that if W is a subspace of an inner product space V that is spanned by a set of vectors S, then a vector u in V belongs to W if and only if u is orthougonal to every vector in S.

Q:

If M is a k-dimensional manifold with boundary, prove that M is a (k - 1) -dimensional manifold and M - M is a k=dimensional manifold.

Q:

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Q:

Please solve Exercise 8. Please only use definitions, propositions, theorems given in the book ''Differential Topology'' by Guillemin and Pollack ! And if you refer to a proposition, theorem or...

Q:

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Q:

Consider a market with one risk-free asset with constant interest rate r and one risky asset that pays no dividends (6 0) the price of which follows dS, S(udtadW1 +a?dW?), So = 1, where . and o 0, i...

Q:

Answer the questions. in the following attachments. Question 1. (10 marks) Consider the function z = f(x, y) = x/y. Showing all steps, use the Newton Quotient approach to find ?z/?y. Question 2. (5...

Q:

Give the typing rules for Peano natural numbers and their eliminator.(ii) Using the rules given above, define the addition function.] (iii) Let a binary tree be either a leaf Leaf or a node...

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

Distribution: 0.2, 0.4, 0.3, 0.1; Observed frequencies: 39, 78, 64, 19; Significance level = 0.05 We have provided a distribution and the observed frequencies of the values of a variable from a...

Q:

Both are bodies of water, but oceans are very large bodies of salt water, while lakes are much smaller bodies of fresh water. Lakes are usually surrounded by land, while oceans are what surround...

Q:

which best fits realize from the following: initial capital investment, a legal share or right in something, lifetime & testamentary transfers, no compulsion to sell, relief from tax obligation,...

Q:

Dr. Terrel H has created a pacemaker that has a rectangular control panel. This rectangle has a width of (Vx +5) millimeters and a length of (Vx +2) millimeters. Find the area in square millimeters...

Q:

Determine a polynomial that represents the area of the figure. m - 5n m+ 5n The area of the figure can be represented by (Simplify your answer.)

Q:

Write an algebraic equation for the following problem and then solve it. Princess Margaret hospital received a shipment of 13-milligram doses of a medicine. Each 13-milligram package was repacked...

Q:

Translate to a quadratic equation, then solve using the quadratic formula. A positive integer squared plus 3 times its consecutive integer is equal to 21. Find the integers. What are the integers?...

Q:

Water + hexane and water + benzene are immiscible pairs. (a) The binary system water + benzene boils at 69.4 C and 760 mmHg. What is the activity coefficient of benzene in water if the solubility at...

Q:

Use the following corn futures quotes: Suppose you sell 18 of the May corn futures at the high price of the day. You close your position later when the price is 467.625. Ignoring commission, what is...

Q:

Rewrite the following two statements using the structure pointer operator: (*rptr).windSpeed = 50; *(*strPtr).num = 10;

Q:

Using the 2001 mortality tables (Table 2 is male and Table 3 is female); find the following probabilities: 1. A male age 20 will die before age 60. 2. Both a male age 60 and a female age 63 will die...