They look like chrome tanned leather to me. If so, they'll always fray and crack a little as they stretch but the leather's usually pretty strong. It's also resistant to sweat so you shouldn't, oil because it doesn't absorb that well, just use a top dressing to give the surfaces some 'slip'.
It's also worth bearing the girth in mind. Modern stainless roller buckles cause less stress on leather than non-rollers, but the worst are chrome or nickel plated. Plain plated buckles rust, giving a rough surface which rubs the leather, and rollers on them often open slightly so you get a sharp edge which isn't very kind, either
It's also worth bearing the girth in mind. Modern stainless roller buckles cause less stress on leather than non-rollers, but the worst are chrome or nickel plated. Plain plated buckles rust, giving a rough surface which rubs the leather, and rollers on them often open slightly so you get a sharp edge which isn't very kind, either