VulkanSharp is one of the newest Vulkan projects for providing bindings for yet another programming language. VulkanSharp is being developed under the Mono umbrella for providing C# / .NET bindings for the Vulkan API.
VulkanSharp is being worked on by Xamarin developers including Jonathan Pryor and Radek Doulik. The VulkanSharp repository was started two weeks ago by Miguel de Icaza. It's not to much surprise that Xamarin is interested in supporting Vulkan via C#/.NET given that it's a cross-platform graphics API and is expected to be heavily used by next-generation Android games/applications, which is a common focus for Xamarin/Mono.
Those wishing to try out the current state of Mono's VulkanSharp bindings, visit this GitHub repository.