Preheat oven to 350 degrees. Line outside of a springform pan with foil to prevent water from seeping in. Have a larger pan ready to use as a bain-marie.
Make Jalapeño Syrup: Combine sugar and water in a small saucepan and bring to boil. Add jalapeños, seeds and all, and simmer over low heat for 10 minutes. Strain and cool. Refrigerate leftover syrup.
Combine 1/3 cup cooled syrup with mango and lime juice in food processor and puree until smooth. Set aside.
Combine cream cheese and sugar in mixing bowl and beat until smooth and fluffy. Add eggs one at a time, beating well after each. Add vanilla, salt and sour cream and blend well. Stir in pureed mango mixture. Pour into springform pan. Place in larger pan. Fill larger pan with hot water. Bake for 45 minutes, and remove both pans from oven and let cheesecake cool in hot water bath. When cool, wrap in plastic wrap and refrigerate until cold. At serving time, carefully remove sides of pan. Decorate top of cheesecake with mango slices if you want.