Differential geometry-imbedded submanifold

Assignment Help Mathematics

Reference no: EM13134344

Let phi : R^2 --> R be a function given by

phi(x,y) = x^3 + xy + y^3 +1

For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2.

( This question was given as part of Differential Geometry course, we use Do Carmo's book,Riemannian Geometry)

Please justify all your steps and claims. And try to solve the problem in a manner similar to the book mentioned above.

Reference no: EM13134344

Questions Cloud

Calculate the molarity of a solution of glycerol : Calculate the molarity of a solution of glycerol made by dissolving 59.000 mL glycerol at 15 degrees celcius in enough water to make 380.00 mL of solution

My glory productions has just finished : My Glory Productions has just finished production of Troubles Ahead, the latest action film directed by Fleur Dunne and starring Rodney Kid and Tess Bow.

Xplain the possible alternatives and the advantages : Stan and Susan, two calendar year taxpayers, are starting a new business to manufacture and sell digital circuits. They intend to incorporate the business with $600,000 of their own capital and $2 million of equity capital obtained from other inve..

Create regression models to predict birth rate : A researcher used stepwise regression to create regression models to predict Birth Rate (births per 1,000) using five predictors: Life Exp (life expectancy in years).

Differential geometry-imbedded submanifold : Let phi : R^2 --> R be a function given by phi(x,y) = x^3 + xy + y^3 +1 For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2.

Define solubility of terpin hydrate for chemistry students : Solubility of Terpin Hydrate for Chemistry Students, what is the structure of terpin hydrate and is it more soluble or less than starting material?

Determine the balance in the finished goods inventory : By the end of November all jobs but RX-115 were completed, and all completed jobs had been delivered to customers with the exception of SL-205. Determine the balance in the Finished Goods Inventory on November 30.

What mass of magnesium chloride can be produced : A mixture of 82.0 g of magnesium (24.31 g/mol) and 350 g of iron(III) chloride (162.2 g/mol) is allowed to react. What mass of magnesium chloride (95.21 g/mol) can be formed?

How would you paraphrase the definition of equilibrium price : How would you paraphrase the definition of equilibrium price?

User Account

All Pages