Rewrite Javascript to jQuery with Ajax

I'm totally new to jQuery and I need to rewrite this bit of javascript to jQuery. Can you help me out? Is this correct?

Javascript:

var xmlHttpRequest = new XMLHttpRequest();

function getTasks(){
var name=document.getElementById("name").value;
var summary=document.getElementById("summary").value;
    if (xmlHttpRequest.readyState==4 && xmlHttpRequest.status==200)
        {
            document.getElementById("open").innerHTML=xmlHttpRequest.responseText;
        }
  xmlHttpRequest.open("Post","jsontaskmanager?name=" + name + "&summary=" + summary, true);
  xmlHttpRequest.send();
}

jQuery:

var xmlhttp = new XMLHttpRequest();

$("document").ready(function(){
    var name = $("name").val();
    var summary = $("summary").val();
    //blah
    $.ajax({
        url: "jsontaskmanager",
        type: "POST",
        dataType: "json",
        data: { name: name, summary: summary },
        success: function(response) {
            $("open").html(response);
        }
    });
});