If you can't find fresh Key limes in your area, you can substitute bottled Key lime juice. Recipe from divinerecipes.com. Springform pan size isn't specified in the instructions, but I think a 9" pan would work just fine.
Preheat oven to 350°F and butter bottom and side of springform pan.
Stir together crumbs, sugar, and butter in a bowl with a fork until combined well, then press evenly onto bottom and one-third up side of pan. Bake crust in middle of oven 8 minutes and cool in pan on a rack.
Reduce oven temperature to 325°F
Beat cream cheese with an electric mixer at medium speed until fluffy, then beat in sugar. Add lime juice, sour cream, and vanilla and beat until smooth. Mix in flour and salt at low speed, scraping down side as needed, until just incorporated, then add eggs all at once and mix just until incorporated.
Pour filling into crust and set springform pan in a shallow baking pan. Bake cake in middle of oven until set in center, 1 hour to 1 hour and 10 minutes. Cool completely in springform pan on rack. (Cake will continue to set as it cools.)
Run a thin knife around edge of cake and remove side of pan. If desired, transfer cake with a large metal spatula to a serving plate.
Peel mangoes and, leaving fruit whole, slice very thinly lengthwise (slightly less than 1/8 inch thick) with mandoline (use caution — peeled mango is slippery). Halve wide slices lengthwise. Gently toss mango slices with lime juice.
Beat cream with sugar in a bowl with electric mixer until it just holds stiff peaks, then spread over top of cheesecake. Bending and curling mango slices, arrange them decoratively over cream.