This is not a female (females have tusks as well). As I understand it, it is common for walruses in captivity to rub their tusks on the bottom of the pool (a natural behaviour considering the animals feeding habits in the wild) and so wear them right down. Sometimes this can lead to infections setting in which requires veterinary interception to remove the remains of the tusk. Moscow Zoo quite famously employ's the International Zoo veterinary Group - Peter Kertez, Andrew Greenwood et al - to carry out this proceedure on their animals. More recent advances in husbandry techniques have allowed zoos keeping walruses to prevent them doing this - I seem to recall hearing it is something to do with the lining of the pool.
Hagenbecks - well known walrus keepers - oddly enough, never had this problem. perhaps someone can elaborate?...